Rambam - 1 Chapter a Day

Some of the requirements mentioned by the Rambam were established by Torah law, while others are Rabbinic ordinances, as explained below.

i.e., is an agricultural product and is neither found naturally—e.g., metals—nor produced from animals nor manufactured synthetically;

and is not still connected to its source of nurture;

This excludes articles used as food and those that have been fashioned into utensils.

As implied by the following halachah, this and the following clause are Rabbinic decrees. S’chach with an unpleasant odor will not create an inviting holiday environment. Indeed, substances with an unpleasant odor should not be used for the sukkah’s walls either.

For a person will not be pleased to have portions of the s’chach falling into his food. The Mishnah Berurah 629:39 states that the prohibition applies to elements that fall off naturally. However, if they fall off only when subjected to wind, there is no difficulty in using them.

for these requirements stem from the Torah itself. The particular aspects of these requirements are described in this and the following halachot.

Sukkah 13a gives the shrub known as hollow as an example of such a substance.

Sukkah 12b gives the plant known as wormwood as an example of such a substance.

For these are only Rabbinic requirements.

Sukkah 13a

the minimum height for a sukkah prescribed in Chapter 3, Halachah..

Sukkah 4a describes this as “a disgusting dwelling, unfit for human habitation.”

The Rambam’s phraseology leaves room for the interpretation that this is a suggestion, but not an absolute requirement. (See Rabbenu Manoach.) Nevertheless, the Shulchan Aruch (Orach Chayim 633:9) states that such a sukkah is unacceptable for use.

even if they have not been made into utensils, but are still in a raw state in which they are unfit to contract ritual impurity;

Even if they are still in a raw state in which they are unfit to contract ritual impurity.

The laws governing the use of such plants as s’chach after they have been hung over the sukkah and then detached from the ground are discussed in Halachah 12.

In particular, this refers to wooden utensils that have a receptacle or are wide and other articles are frequently placed upon them—e.g., a table. However, wooden utensils that do not fall into these categories are not subject to contracting ritual impurity, and, hence, may be used for s’chach. An example of such utensil is a ladder. The Rambam (Hilchot Keilim 4:1) declares that a ladder is not subject to contracting ritual impurity. Hence, according to his opinion, there is no difficulty with using it as s’chach.
(It must be emphasized that other authorities question the Rambam’s decision on a ladder and maintain that a ladder may be subject to contracting ritual impurity. Hence, it is preferable not to use it as s’chach. See the Shulchan Aruch and Ramah, Orach Chayim 629:7.)

However, mats that were made for use as s’chach or for shade may be used as s’chach. Halachah 6 discusses the laws which apply when a mat was made without any specific intention.

e.g., utensils with holes of sufficient size to render them no longer subject to contracting ritual impurity. (See Hilchot Keilim, Chapter 6.)

e.g., garments that have worn out and are less than three fingerbreadths by three fingerbreadths in size and, hence, are no longer subject to contracting ritual impurity (Sukkah 16a; Hilchot Keilim 22:21).

This is a Rabbinic decree on the basis of the following rationale...

previously,

I.e., when a utensil is broken and no longer fit to be used for its initial purpose, it is no longer susceptible to ritual impurity. At times, however, a utensil may be only partially broken and a question exist whether it is susceptible to ritual impurity or not.

This refers only to foods for humans. Food which is eaten primarily by animals is not subject to contracting ritual impurity (Hilchot Tum’at Ochlin 1:1) and hence may be used as s’chach (Taz 629:12).

There is a slight imprecision in the Rambam’s statements. Produce is not subject to contracting ritual impurity until it comes into contact with liquid. (See Leviticus 11:38; Hilchot Tum’at Ochlin 1:1-2.) Nevertheless, foods are not fit to be used as s’chach even though they have never come into contact with water (Shulchan Aruch HaRav 629:1; Mishnah Berurah 629:28).

I.e., the difficulty being that although the branches are proper s’chach, the fruit is unfit to be used for that purpose.

i.e. branches and leaves

i.e. fruit

Rabbenu Manoach explains that these decisions are based on the principle that according to Torah law, mixtures are categorized according to the majority לטנ(.) ברב
On the basis of Sukkah 13b-14a, the Shulchan Aruch (Orach Chayim 629:10) explains that sometimes the stems of the fruit are considered part of the fruit, and on other occasions part of the branches. The Magen Avraham 629:12 explains that generally, a ste1h is not considered to be longer than three handbreadths. However, there are certain instances (e.g., grains) when a longer measure is considered. Hence, it is proper to be stringent in this regard. (See also Shulchan Aruch HaRav 629:15-16.)
The apparent contradiction between this halachah and Halachah 13 is discussed in the commentary on that halachah.

The Maggid Mishneh explains that this refers to vegetables that are used as animal food, and hence were not excluded by the previous clause of this halachah. Rabbenu Manoach and the Shulchan Aruch (Orach Chayim 629:12) explain that this refers to vegetables that are eaten by humans. Sukkah 13b appears to support the latter interpretation, stating:
The vegetables with which a person can fulfill his obligation on Pesach... [can] invalidate a sukkah, [because they are considered] to be vacant space.

i.e., the vegetables will dry up and wither during the Sukkot festival, leaving the sukkah with more vacant space than shade (Kessef Mishneh).

According to the Maggid Mishneh’s interpretation, the explanation of the law is straightforward. It teaches us that rather than consider the vegetables to be non-kosher s’chach, we consider their space to be vacant. The latter interpretation requires a slightly more intricate explanation. The vegetables are not considered to be non-kosher s’chach, which would invalidate the sukkah if they take up four handbreadths, as explained in Halachah 14. Rather, their space is considered to be empty. Hence, a space of three handbreadths is sufficient to invalidate the sukkah, as explained in Halachah 20.

The use of the word עץ, rendered as branches or wood, with regard to flax, has its source in Joshua 2:6, which describes how Rachav “hid them in branches of flax.”

The Rishon Letzion questions the law when the flax has been crushed but not combed, and concludes that as long as it has not been combed, it is acceptable. Nevertheless, Shulchan Aruch HaRav 629:5 does not accept this conclusion.

Though it is not considered to be a garment and, hence, is not subject to contracting ritual impurity (Maggid Mishneh; see also Shabbat 27b), it may nevertheless not be used as s’chach...

The Ra›avad disagrees with this principle and states that even before it is woven into a garment, flax is useful to stuff pillows and covers. Hence, it is subject to contracting ritual impurity and is thus unfit to be used as s’chach.
The Maggid Mishneh points out a contradiction to the Ra’avad’s logic. The “male arrows” mentioned in the following halachah are—like flax—prepared to be used for a purpose. Nevertheless, they are considered acceptable for use as s’chach.
Rav Kapach mentions two possible extensions of the difference of opinion between the Rambam and the Ra’avad: a) paper or carton—According to the Rambam, it may not be used because it no longer resembles a plant produced from the earth. According to the Ra’avad, it might be acceptable, since it is not subject to contracting ritual impurity. b) cotton wool—It may be used for the purposes mentioned by the Ra’avad and thus, according to his opinion, would be subject to contracting ritual impurity. Nevertheless, its natural form is preserved. Hence, according to the Rambam’s opinion, it would be acceptable. (It must be noted that the Magen Avraham 629:3 and Shulchan Aruch HaRav 629:5 maintain that after cotton has been combed, it is considered as though its form has been altered.)

Nor are they susceptible to ritual impurity.

The question whether the arrows are acceptable as s’chach or not revolves around their susceptibility to contracting ritual impurity.

i.e., the end of their body is sharpened and comes to a point, which is intended to be put inside a metal arrowhead.

for the arrow itself is considered a simple wooden utensil which is not susceptible to contracting ritual impurity. (See Hilchot Keilim 1:10.)
The Magen Avraham 629:.2 states that this decision applies only before these arrows were placed in the arrowhead. If they have been placed in the arrowhead, even if subsequently removed they are no longer acceptable as s’chach.

i.e., the end of their body is hollowed out for the arrowhead to be inserted within

Since the end of the arrow is hollowed out for the arrowhead to be inserted, they have usage as a receptacle, and are susceptible to ritual impurity.

Hilchot Keilim 2:3 states: “A receptacle which is made to be filled is not considered a receptacle.” Thus, one might assume that these arrows would also not be considered as having a receptacle. The Pri Ha’aretz explains that since the iron arrowheads are often removed from these bodies, it is considered as though...

It must be noted that Rashi and other commentators follow the simple interpretation of Sukkah 12b (the source for this law) and disagree with the Rambam’s decision in Hilchot Keilim. They maintain that if a utensil has a receptacle, even if it will be permanently filled, it is subject to contracting ritual impurity.

The conimentaries note an apparent contradiction in the Rambam’s words. Hilchot Keilim 25:13 states that even a small mat of reeds or hemp is not subject to contracting ritual impurity, because it is uncomfortable to lie on.

Since the mat was made with that specific intention, we do not follow the general principles, but rather judge it individually.

1he Rambam’s statements are based on Sukkah 20a. It must be noted that his decisions are dependent on the version of the text of the Talmud he accepted. The Ra’avad and others interpret the word גדולה as related to the word גדיל (tassel). Thus, they explain that the Talmud is referring to a small mat. However, because it is made of thick tassels, rather than woven, it is not comfortable to lie on, and hence would most likely be used for shade. According to this opinion, any woven mat, even if it is large, is unfit to be used as s’chach. The Shulchan Aruch (Orach Chayim 629:6) quotes the Rambam’s interpretation.

The Ramah (Orach Chayim, ibid.) mentions that in places where it is customary to affix mats permanently as the roofs for homes, they may not be used for s’chach. The Rabbis instituted this decree lest people remain in their homes on Sukkot without differentiating between them and a sukkah.

i.e. a frame

Tosafot, Sukkah 20b quotes Ketubot 50b, which explains that such mats were used to collect dates.

which, as explained in Halachah 2, may not be used as s’chach even though they are not susceptible to contracting ritual impurity.

In many places throughout the Talmud, four handbreadths is established as the minimum size of an area. Hence, a board of that size is considered significant and may not be used as s’chach (Sukkah 14a).

smooth, and thus are fit to be used in their present state (Sukkah 15a; Rabberiu Manoach).

A person might think: “What is the difference between the sukkah and my house—they are both covered with boards?” This is surely a false assumption. As explained in the following halachah, since the boards of a roof were not placed there for the purpose of shade, but rather to be part of the permanent structure of the. house, they cannot be considered to be s’chach (Sukkah 14a; Rabbenu Manoach).

The Kessef Mishneh explains that this law applies only when the sukkah already possesses its minimum size without the board. Shulchan Aruch, Orach Chayim 632:1.

According to the Maggid Mishneh, because it is part of the wall; according to the Kessef Mishneh, because it appears to be a separate domain.

or fulfilled any other of the activities which must be performed in the sukkah

Sukkah 14b explains th, after the Sages forbade the use of such boards, they are considered to be equivalent t iron poles.
The Magen Avraham 629:22 writes that at present it is customary not to use boarc as s’chach, even if they are less than four handbreadths wide. However, if there is no other s’chach available, one may use boards for that purpose even if the are more than four handbreadths wide.

as required by the following halachah

performed two activities:

from their place. (Though the Shulchan Aruch, Orach Chayim 631:9 does not mention this requirement, the Mishnah Berurah 631:4 does.)

holding the boards in position. (See the Rambam commentary on the Mishnah, Sukkah 1:7.) Through these actions, one is considered to have nullified the previous placement of the boards, and it is considered as though they have been placed there...

Therefore

for the boards are essentially fit to be used as s’chach. The only difficulty was the intention with which they were originally placed. A change of mind without an act is not sufficient, since, as explained in the commentary, on the following halachah, we are required to “make” a sukkah and not use one which has already been made.

as explained in the previous halachah. Rabbenu Asher states that in such a situation, the sukkah is acceptable even though the boards are more than four handbreadths wide.
He explains that in the previous instance, the reason the Sages forbade using such boards was to differentiate between them and the boards of a house. In the present instance, the fact that the person took apart the roof of his house obviously implies that he realizes that it may not be used as a sukkah. Hence, there is no need for such a decree. This opinion is accepted by the Shulchan Aruch, ibid.

The Magen Avraham 631:8 explains that in this instance, even the Rambam would allow the boards that remain to be more than four handbreadths in width. The requirement of placing kosher s’chach obviously implies that the use of the boards of a roof as s’chach is unacceptable. However, many other authorities do not accept this interpretation of the Rambam’s position.

Sukkah 8b quotes a baraita which contains the latter statement and questions: “What does ‘according to law’ mean?... That it was made for the purpose of shade.”
It appears that the Rambam uses the same expression, but with different implications. Since he explicitly states that the sukkah must be constructed for the purpose of shade, one might infer that the expression “according to law” is intended to include other concepts. Thus, it can be a reference to the requirements for a sukkah’s size and the nature of the materials used for the s’chach, as mentioned in this and the previous chapter.

The Mishnah, Sukkah 1:1, states: An old sukkah: The School of Shammai deems it unacceptable, while the School of Hillel rules it kosher.
The commentaries explain that the term “an old sukkah” refers to any sukkah that was constructed for purposes other than the fulfillment of the mitzvah.
In its discussion of this law, the Jerusalem Talmud requires that one must make an addition or change to the s’chach. Though that decision is not quoted by the Rambam, Rabbenu Asher mentions it and it is accepted by the Shulchan Aruch (Orach Chayim 636:1). Nevertheless, the Magen Avraham 636:1 explains that this is a desirable and proper step, but the sukkah is acceptable even though no changes have been made.

Isaiah 4:6 states: “It shall be a sukkah for shade from the heat...” thus defining the purpose of such a structure. A sukkah constructed for the purposes of modesty is not acceptable (Rabbenu Manoach).

which are outside the entire framework of mitzvot. Sukkah 8b also mentions the sukkot made for shepherds and watchmen. Though the latter are obligated to keep the mitzvah of sukkah, they did not necessarily construct their sukkot with that intent in mind.

E. g., branches fell over a frame.

Sukkot 12a explains that there is an added factor involved in this example. Deuteronomy 16:13 states: “Make a [celebration of] the Sukkot holiday for seven days.” This refers to the construction of the sukkah and teaches that we must “make” a sukkah and not use what was already made. Therefore, despite the fact that the person hollowed out the space for the purpose of shade, the sukkah is not acceptable, because the produce was not originally placed there for that purpose.
We find a similar principle concerning tzitzit. Deuteronomy 22:12 states: “Make yourself tassels on the four corners of your garments.” On the basis of this command, Menachot 40b teaches that it is unacceptable to tie tzitzit to a three-cornered garment and then cut a fourth corner, since we are required to make tzitzit, and not use what is already made.

The Ba’al Hamaor writes that if, originally, a person were to pile produce with the intention that later he would hollow out a sukkah, the sukkah would be acceptable. However, this opinion is not accepted by other authorities.

We find the measure of one handbreadth considered to define a structure with regard to the laws of ritual impurity. Accordingly, it is given significance in this context as well. (See Sukkah 16a.)

by seven handbreadths

i.e. for shade

the minimum height of a sukkah, as explained in Chapter 3, Halachah 1.

and then, the original structure was merely expanded.

Although, according to the Torah’s requirements, these would be considered proper s’chach...

by the Sages (Sukkah 12a)...

which is unacceptable; as explained in the previous halachah.

placed bundles of these substances on a roof with the intent that they would be used as s’chach and...

The Shulchan Aruch (Orach Chayim 629:17) explains that a different rule applies if the bundles were originally placed on the roof to dry out. For them to be acceptable as s’chach, untying them alone is insufficient, and one must also shift the position of their contents.

Thus, any lesser amount of these substances are acceptable as s’chach even though they are tied together.

The Kessef Mishneh questions the reason for the addition of the adjective, noting that if the bundles contain fewer than twenty five units, they are permitted, as stated in the previous halachah. Others mention that this refers to bundles of small branches.

to be untied immediately thereafter (Shulchan Aruch, Orach Chayim 629:16).

Sukkah 13b relates that bundles of this nature were frequently used in Sura, and that the Sages permitted them to be used as s’chach.

The Ba’al Hamaor questions whether this principle applies only with regard to s’chach, where it is logical to assume that a more lenient position would be taken, since the entire question revolves around a Rabbinic decree, or whether it also applies in all cases where Torah law itself requires a bundle.

However, if one were to add even one branch and then tie them together, it would be considered to be a bundle (Shulchan Aruch, Orach Chayim 629:15).

Sukkah 13b mentions this principle when explaining why bundles of willows whose upper tie was loosened could be used as s’chach.

and the sukkah is unacceptable. This applies only when the shade the tree produces exceeds the open area. However, if there is more open space under the tree than shade, the sukkah may be kosher.
The determination of whether such a sukkah is kosher depends on a number of principles, based on the interpretation of Sukkah 9b and 11a. The Rambam’s interpretation of that passage, and thus the ground rules he · establishes, differ from those accepted by the Shulchan Aruch (Orach Chayim 626:1-2).
In the following halachah, the Rambam deals with the resolution of the question when no effort has been made to correct the problem of the non-kosher ‘s’chach. As will be explained, there his interpretation is contested by other authorities. In this halachah, the Rambam describes the rulings which govern the situatiori when an effort has been made to rectify the situation by detaching the branches from their source of-nurture. These are based on the Mishnah, Sukkah 11a, and are also accepted by other Rabbinic authorities. (See the Shulchan Aruch, Orach Chayim 626:2.)

As mentioned in Halachot 1 and 2, branches are fit to be used for s’chach only after they have been detached from their source of nurture.

Though at present, the branches would be acceptable as s’chach, as explained in the commentary on Halachah 9, the Torah requires that when s’chach is originally put in place, it must be kosher. Otherwise, it is unacceptable even though steps were taken to correct the disqualifying factors. This is based on the principle that one must make a sukkah and not use one which is already made.
Nevertheless, since the prohibition against using these branches as s’chach does not relate to their essential nature, their presence may be nullified when there is a majority of kosher s’chach. This conforms to the principle of לרזפיב. ברב

the presence of the branches remains halachically significant. Hence,...

I.e., each of the branches individually (Shulchan Aruch, ibid.).

Moving the branches negates their previous placement, and afterwards they are considered to be kosher s’chach, which was put in place for the purpose of creating a sukkah.

This may refer to a substance like metal, which is unfit for use as s’chach because it does not grow in the earth, or branches of a tree which have not been detached from their source of nurture.

The presence of the substance which is not acceptable as s’chach is not nullified according to the principles of ביטול ברב, because it exists as a separate entity which can be distinguished from the kosher s’chach.
Rav Avraham, the Rambam’s son, notes the apparent contradiction between this decision and Halachah 3, which states:
[When one uses] branches from a fig tree which contain figs,... We see if the waste is more than the food; then we may use them as s’chach.
That halachah also mentions kosher s’chach—the branches—and substances which are not acceptable as s’chach—the figs. However, if there is a greater quantity of branches, the presence of the figs is nullified. In contrast, in this halachah, that concept is not applied.
Rav Avraham distinguishes between the two. In Halachah 3, the person does not intend to use the fruit for the purpose of shade; he merely wants to save the effort of removing it from the branches. Therefore, their presence may be nullified. In contrast, in this halachah the substances which are not acceptable as s’chach are being employed for the purpose of shade itself. Hence, their presence cannot be nullified.

As mentioned above, this decision depends on the Rambam’s interpretation of Sukkah 9b. That passage reads:
A person who constructs his sukkah under a tree is considered as though he built it within his home...
Ravva said: “The above applies only to a tree whose shade is greater than its open space. However, if its open space is greater than its shade, it is kosher. What difference does it make if its open space is greater than its shade, the substance not acceptable as s’chach will be combined with the kosher s’chach [and therefore, the sukkah will not be acceptable]?
Rav Pappa said: בשחבטן.
The Maggid Mishneh, the Ra’avad, and Rabbenu Manoach explain that the Rambam renders בשחבטן as “when he separated them.” Thus, when the two substances were combined, the Rambam’s opinion would be that the sukkah is not kosher, as explained in this clause of the halachah. When they are separate, the sukkah may be kosher according to the stipulations mentioned in the following clause of this halachah and the halachot to come.
(The Kessef Mishneh explains that the Rambam renders בשחבטן as “when he severed them.” However, that difference in interpretation does not result in a difference in halachah.)
Rashi and others interpret בשחבטן as “when he lowered them (and mixed them together with the kosher s’chach).” Thus, according to this opinion, the sukkah is acceptable when the kosher and non-kosher s’chach are mixed together. Thus, this view is diametrically opposed to the ‘Rambam’s, who maintains that such a mixture is of no avail.
As noted by the Shulchan Aruch (Orach Chayim 626:1), there are two ways of understanding this interpretation of the passage. However, since both of them are not acceptable to the Rambam, their explanation will not be included here.

When there is a majority of kosher s’chach, it is judged to be an independent entity. When there is a sufficient amount of kosher s’chach, the sukkah is kosher unless the substance that is not acceptable as s’chach is placed in a manner which can disqualify the entire sukkah, as is explained in this and the following three halachot.

The principle of l’vud, by which this substance could be considered to be a continuation of the kosher s’chach, cannot apply. However, if there is less than three handbreadths of the substance that is not acceptable as s’ chach in one place, even though there are a number of such patches among the s’chach, the sukkah is kosher, as stated in Halachah 16. Furthermore, one may eat and sleep under the non-kosher s’chach (Shulchan Aruch, Orach Chayim 632:1).

the substance which is not acceptable as s’chach is placed...

The principle of l’vud, by which this substance could be considered to be a continuation of the kosher s’chach, cannot apply. However, if there are less than three handbreadths of the substance that is not acceptable as s’chach in one place, even though there are a number of such patches among the s’chach, the sukkah is kosher as long as the majority of the s’chach is kosher, as stated in Halachah 16.

See the commentary on both the previous and following halachot.

which possesses a minimal amount of kosher s’chach, more lenient rules apply...

across the entire span of the sukkah, dividing the sukkah in half, it is considered to be significant (Rashi, Sukkah 17a), and hence the sukkah is disqualified.
The Ramah (Shulchan Aruch, Orach Chayim 632:2) emphasizes that even where the non-kosher s’chach is of this size, if the sukkah possesses seven cubits by seven cubits of kosher s’chach in one place, that portion may be considered to be a kosher sukkah and used during the holiday.

the division is not as noticeable. Hence,

The Shulchan Aruch (Orach Chayim 632:1) states that one may eat and sleep throughout the entire sukkah. However, the Ra’avad and Rabbenu Nissim do not accept this leniency, and the Mishnah Berurah (632:3) advises following this stringency.

Four cubits or more exceeds the measure of leniency provided by the Torah.

On the basis of the principle of דֹּפֶן עֲקֻמָּה explained below.

This and the following examples are given by the Mishnah, Sukkah 1:10.

note the drawing accompanying Chapter 4, Halachah 8.

Sukkah 17a explains that one might not necessarily have been able to deduce this example from the previous one, because in that instance the walls of the house were constructed for it. In contrast, the walls of the excedra were not constructed for its sake, but for the houses on either side.

Sukkah 17a explains that one might not necessarily have been able to deduce this example from the previous ones, because in those instances only kosher s’chach was placed over the opening of those structures. In this instance, a substance that is not acceptable as s’chach was placed on the roof intentionally.

Rabbenu Nissim states that this law applies only when the walls reach all the way to the s’chach. Otherwise, it is impossible to consider the non-kosher s’chach to be an extension of the walls. · The Tur and the Taz quote more lenient positions and allow such a sukkah, even though the walls do not reach the s’chach.

Though the sukkah as a whole is kosher, one may not eat or sleep under the non-kosher s’chach if it is four handbreadths or more in size (Shulchan Aruch, ibid.). The rationale behind this decision is that the non-kosher s’chach is considered to be part of the wall and not part of the s’chach.

The latter term refers to a law that was transferred from generation to generation reaching back to Mount Sinai. Nevertheless, there is no mention of—or even direct allusion to—it in the written Torah.

referred to in the previous two halachot and in Halachah 20

As explained above, if there are three handbreadths or more of non-kosher s’chach in one place, the principle of l’vud cannot apply. Hence, the sukkah is not kosher, because it lacks. the minimum amount of s’chach (Sukkah 17a). However, if there is less than that amoant of non-kosher s’chach, the non-kosher s’chach is included as part of the sukkah and is counted as part of its minimum size (Shulchan Aruch, ibid.).

Since it· is of sufficient size, it will be disqualified only when it is divided in half by a significant portion of non-kosher s’chach, or when it is too far, i.e., more than four cubits, removed from the walls.

so that even in a small sukkah, all the conditions mentioned in the above halachot are met, there is a further requirement before the sukkah is considered kosher.

This concept can be derived from the Mishnah (Sukkah 1:8): “If someone places iron staves or the frames of a bed as the roof of his sukkah, it is kosher, provided there is an equivalent amount of empty space”
In his commentary on that Mishnah, the Rambam emphasizes that the word “equivalent” should be interpreted loosely, since there must be more kosher s’chach than the non-kosher s’chach.

This decision has raised questions from all authorities. Though the Rambam’s decision is based on Sukkah 15a, Eruvin 15b states that a divider whose open portion is as great as its closed portion is considered to be a divider. Indeed, the Rambam himself quotes that decision in Hilchot Shabbat 16:16. If so, why does he not follow the same principle in this instance as well?
The Kessef Mishneh explains that the Rambam’s decision is based on the fact that there is no way that there will not be some tiny open spaces within the kosher s’chach of a sukkah. Accordingly, even if the kosher s’chach is equal in area to the non-kosher s’chach, the tiny spaces between the kosher s’chach will tip the balance in favor of the non-kosher s’chach.
The Shulchan Aruch, Orach Chayim 631:8 quotes the Rambam’s decision as halachah, but adds as a reason (a quote from Rabbenu Tam’s text of Sukkah 15b): “for it is impossible to be exact.” This implies that were it possible to know that the kosher s’chach is exactly equal to the non-kosher s’chach, it would be acceptable. See also commentary to Halachah 19.

in a small sukkah, or four handbreadths in a large sukkah.

The Tzafnat Paneach questions the phraseology used and renders the latter phrase as “the non-kosher s’chach is considered as an open area;” i.e., as an entity by nature unfit for a sukkah and not as mere empty space. Note Halachah 20, which differentiates between the two and states that the measure of open space which disqualifies a sukkah is less than that of non-kosher s’chach.

for added shade (Sukkah 1:3)

the bracketed additions are based on the Rambam’s commentary on that Mishnah.

The cloth nullifies the presence of the kosher s’chach above or below it.
(Tosafot explains that as long as the sukkah has sufficient s’chach without the cloth, the cloth will not necessarily nullify the presence of the kosher s’chach. However, the majority of the halachic authorities and the Shulchan Aruch, Orach Chayim 629:19 do not accept this view.)
However, once the cloth is lifted away, the kosher s’chach is acceptable without any further activity. (See Ramah, Shulchan Aruch, Orach Chayim 626:3.) Thus, a roof can be constructed to protect a sukkah from rain, provided it is removed while the sukkah is being used.

For a decoration is considered to be an extension of the article it adorns.

Rabbenu Manoach emphasizes how the s’chach should be set in place before the decorations. Otherwise, they could be considered as intervening substances.

Sukkah 10a describes the decoration of a sukkah with tapestries, nuts, pomegranates, grapes, and flasks of wine, oil, and flour.

and one is permitted to eat and sleep under the decorations.

I.e., if the inner space of the sukkah is more than twenty cubits high and the sukkah is therefore not acceptable (Chapter 4, Halachah 1), the presence of the decorations is not considered significant to reduce that space to the legal requirements.

Thus, the sukkah must have a full seven by seven handbreadths of open space besides them.

as mentioned frequently above, four handbreadths constitutes a significant space

they are considered to be non-kosher s’chach, and if they are of the size mentioned in Halachot 13 and 14...

See Chapter 5, Halachot 1 and 2.
The Taz (627:5) cautions against hanging any decorations more than four handbreadths away from the s’chach regardless of how small they are.

and of course, if it is more than

Although the sukkah should be acceptable as long as the covered portion is equal to the open portion, in this situation...

Sukkah 22b explains that light spreads out. Accordingly, even though on the roof the portion covered by s’chach is equal to the uncovered portion, on the ground the area exposed to the sun will be greater than the shaded area. See also the Rambam’s commentary on the Mishnah, Sukkah 1:1.

As mentioned in Halachah 9, a sukkah must be constructed for the purpose of shade. If the portion exposed to the sun is greater than the shaded portion, it obviously does not serve that purpose.

On the surface, the Rambam’s choice of phraseology is slightly inexact, because everything depends on the amount of shade on the ground.

To disqualify the sukkah, the empty space must extend across the entire span of the sukkah or create a place large enough for a person to stand in (Tosafot, Sukkah 17a; Ramah, Shulchan Aruch, Orach Chayim 632:2).
Furthermore, if the sukkah area is more than seven handbreadths by seven handbreadths in addition to the open space, the remaining covered area of the sukkah is kosher.

Any space less than three handbreadths can be considered to be part of the s’chach on the basis of the principle of l’vud.

i.e., an empty space cutting the sukkah in two

I.e., an empty space cutting the sukkah in two, or an empty space that runs from one corner of the sukkah to the other.

Non-kosher s’chach and open space are two different halachic categories. They have different measures with which they each disqualify a sukkah, and combinations of the two are not considered to be a single entity. Thus, if there is an open space three and a half handbreadths wide, one may correct the sukkah by putting one handbreadth of non-kosher s’chach in its place. (See the Shulchan Aruch, Orach Chayim 632:3.)

The terms “large” and “small” are explained in Halachot 13-15.

because the sukkah has less than seven handbreadths by seven handbreadths of kosher s’chach.

I.e., there are two portions of the sukkah, one which is mostly shaded and one which is mostly exposed to the sun.

when the sukkah is taken...

and one may eat and sleep in the part of the sukkah where the portion exposed to the sun exceeds the shaded portion (Magen Avraham 631:1). The Ramah quotes a more stringent opinion which forbids using the portion with more sun if it is seven handbreadths by seven handbreadths in area.

Shulchan Aruch HaRav (631:5) uses the expression לכתחילה—i.e., one should set out to construct a sukkah in this manner.

From the Jerusalem Talmud, Sukkah 2:3, the source for this statement, it appears that the expression “large stars” means stars large enough to be seen during the day.

The latter expression is quoted from the Mishnah, Sukkah 2:2.

Shulchan Aruch HaRav (631:5) uses the expression בדיעבד (after the fact), implying that it is not desirable to construct a sukkah in this manner. Nevertheless, the Mishnah Berurah (631:5) quotes many Ashkenazic authorities who tend toward making the s’chach thick.
The above applies only with regard to placing the s’chach. However, afterwards, even when the s’chach is thick, a person should have no compunctions about using such a sukkah.
Though thick s’chach is kosher, the Magen Avraham 631:2 notes that if it is so thick that rain will not enter the sukkah, the sukkah is unacceptable, because then it resembles a house and not a temporary dwelling made for shade.

Sukkah 22a questions: “What is the meaning of the word מדובללת used by the Mishnah?” Shmuel (whom the halachah follows) replies: “One reed going upward and one reed going downward.”

Even though there will gaps in the s’chach and during certain times of the day, when the sun shines at an angle, the portion of the sukkah exposed to the sun will exceed the shaded portion (Ramah, Orach Chayim 631:5).

As explained previously, any distance less than three handbreadths is not significant because of the principle of l’vud.

by a handbreadth, the minimum size of a roof. (See Chapter 4, Halachah 7.)

This principle, referred to by Sukkah 22a as חבוט רמי—literally, “cast it down”—is one of the leniencies followed as a halachah received from Moses on Mount Sinai. It allows this uneven roof to be considered to be a single straight entity. The same principle is also applied in Hilchot Shabbat 15:25 and Hilchot Tum’at Meit 16:5.

i.e., that the upper portion could be lowered into the space left open by the lower portion. However, if it would not fit exactly in between the spaces, this principle does not apply (Kessef Mishneh). The Lechem Mishneh, noting the Rambam’s decision in Hilchot Shabbat, explains that even if the lower space is wider than the upper portion, as long as they do not overlap, it is acceptable.
The Merchevat Hamishneh explains that the law differs, here from Hilchot Shabbat, because there is a principle that two halachot received from Moses on Mount Sinai cannot be used simultaneously to have a sukkah considered to be kosher.
In the Shulchan Aruch (Orach Chayim 631:5), Rav Yosef Karo quotes the opinion he stated in the Kessef Mishneh. However, Shulchan Aruch HaRav (631:7) and others follow the view of the Lechem Mishneh.

Sukkah 9b explains that the verse which commands us to dwell in sukkot (Leviticus 23:42) spells the word—סכת—omitting the letter ו, which is usually used. On that basis, the Sages explained that a single structure may be used for one sukkah, but not for two. Of the two, the lower sukkah is disqualified because...

since the floor of the upper sukkah is its roof, it may not be considered to be s’chach, because it was not placed there for purposes of shade alone, nor can the lower sukkah be acceptable because of the s’chach of the upper sukkah, for the floor intervenes between them.

There is no reason that the presence of the lower sukkah should disqualify it.

the minimum height of a sukkah, as explained in Chapter 4, Halachah 1.

Otherwise, the upper sukkah is not fit to dwell in. Though a sukkah is only a temporary dwelling, it must be fit to be used for all the purposes for which one uses one’s home, as explained in Chapter 6, Halachah 5.

i.e., even if the floor of the upper sukkah shakes when pillows and covers are placed on it (Rambam’s commentary on the Mishnah. Sukkah 1:2).

and thus, is unfit to be used.

The use of this word is questionable. It implies that both sukkot, the upper and the lower one, are kosher. The Kessef Mishneh states that if the upper sukkah is not fit to dwell in, it is not kosher, and therefore recommends striking the word “even” from the text. Though the Lechem Mishneh attempts to justify the use of the term, his arguments seem forced. However, it must be noted that most manuscripts and printings of the Mishneh Torah as well as the Rambam’s and most other texts of the source for this halachah—the Mishnah, Sukkah 1:2—include this word.

For the reason that since its roof is of no functional purpose, it is not considered an intervening substance between the sukkah and the upper s’chach.

the maximum height of the sukkah, as stated in Chapter 4, Halachah 1.

In the Kessef Mishneh—and also in the Shulchan Aruch (Orach Chayim 628:1)—Rav Yosef Karo explains that this applies only when the s’chach of the lower sukkah is not substantial enough to allow the use of the sukkah. However, if the s’chach of the lower sukkah alone produces enough shade to permit the use of the sukkah, it is kosher even though the s’chach of the upper sukkah is more than 20 cubits high.
He continues to explain that even though the presence of non-kosher s’chach nullifies the kosher s’chach below it, that applies only when the substance used is by nature not acceptable for use as s’chach. In this instance, the s’chach of the upper sukkah is fit to be used; the only difficulty is its position: its placement above the maximum height of the sukkah.
(Though this concept is found in Tosafot, Sukkah 9b, no allusion to it appears in the Rambam’s statements. Indeed, the simple meaning of the Rambam’s words implies the very opposite. Furthermore, in his commentary on the Mishnah [Sukkah 1:1], the Rambam explains that the reason s’chach placed higher than 20 cubits is unacceptable is that it makes the sukkah into a permanent dwelling. Thus, according to the Rambam, such s’chach can be compared to the boards of a house, which though originally kosher for use as s’chach, are disqualified because they became part of a permanent structure.)

the minimum height for a dwelling to be considered to be an · independent structure (Sukkah 20b).
In this and the following instances mentioned in this halachah, the ten handbreadths are measured from the ground to the canopy (Shulchan Aruch HaRav 627:2-3; Mishnah Berurah 627:5).

The Mishnah, Sukkah 2:1 relates:
An incident occurred concerning Tavi, Rabban Gamliel’s slave. He would sleep under a [canopied] bed [in the sukkah]. Rabban Gamliel told the Sages: “See my slave, Tavi. He is well-learned and knows that slaves are free of the obligation of [dwelling in] the sukkah. Hence, he sleeps under a bed.”

with non-kosher s’chach

even if it has no walls (Shulchan Aruch HaRav 627:1)

placed over a bed

As mentioned frequently above, a handbreadth is the minimum measure of a roof.

or perform any other activity required to be performed in a sukkah. (Perhaps the Rambam mentions sleeping because it is an activity that may be performed only within a _ sukkah. Even a short nap should not be taken outside the sukkah. In contrast,. a snack may be eaten outside a sukkah.)

for the same reasons mentioned above.

Hence, we are forbidden to use the space below it as a sukkah.
This halachah depends on the Rambam’s interpretation of the Mishnah, Sukkah 1:-3. However, Tosafot, Sukkah 10b and the Shulchan Aruch (Orach Chayim 627:3) interpret the passage differently and forbid spreading a canopy over bedposts which are permanently affixed to the four corners of a bed, even if the canopy is less than ten handbreadths above the ground.

Tosafot (ibid.) and the Shulchan Aruch (ibid.) differ with this decision as well, and explain that if these pillars are ten handbreadths high and permanently affixed to the bed, it is forbidden to spread a sheet over them.

If the canopy is not permanently affixed to the bed, even Tosafot and the Shulchan Aruch will permit its use.

i.e., even if they are more than ten handbreadths high.

Sukkah 19a relates that Abbaye found Rav Yosef sleeping in a canopied bed in the sukkah. The latter explained that the canopy he was using was permitted because it did not have a roof.

As stated in Chapter 4, Halachah 7, such structures are not acceptable for use as a sukkah. Hence, they also cannot disqualify a sukka:h.

Although, as stated in Chapter 8, Halachah 10, a person cannot fulfill the mitzvah of lulav as prescribed by the Torah with a lulav belonging to a colleague, that concept does not apply with regard to a sukkah.
Sukkah 27b explains the derivation of this concept as follows: Leviticus 23:42 states: “Every citizen of Israel shall dwell in sukkot.” The latter word is written סכת, implying one sukkah. This prompted our Sages to declare: “All Israel are fit to dwell in a single sukkah.”
In his commentary, Rashi explains that the cost of such a sukkah would not be high enough to require every individual to pay a penny’s worth. Hence, we must assume that some people would be using a borrowed sukkah, and, nevertheless, our Sages said that it was kosher.

There is a siight imprecision with the Rambam’s statements. A stolen object which the thief is obligated to return cannot be used to perform a mitzvah, because it is considered a mitzvah that came about through a sin (מצוה הבאה בעבירה) However, in the instances cited by the Rambam, the sukkah itself is never considered stolen property. Hence, the use of such a sukkah is not forbidden. However, in a number of instances (see below), the sukkah itself is considered to be stolen property and must be returned. Hence, it cannot be used to fulfill the mitzvah.

Since the sukkah is built on the land, it is considered part of the property and the above rule applies to it as well. Thus, the sukkah is still considered to be the property of its original owner and the thief is viewed as merely “borrowing” the sukkah from him, and a borrowed sukkah is permitted.

Sukkah 31a relates that a woman once came to Rav Nachman complaining that the exilarch’s servants had stolen wood from her to build his sukkah.
Rav Nachman answered that they had, nevertheless, fulfilled their obligation...

but not the wood itself. Thus, the sukkah itself is the property of the thief. Though he is obligated to pay the owp. er for his wood, that obligation does not prevent the sukkah from being considered as his.
Hilchot Gezeilah 1:5 explains this principle by stating:.
Anyone who steals is obligated to return · the stolen property itself... If it was lost or changed, he is obligated to return
its monetary value...
Even if one steals a beam and builds a mansion [using it], since [the beam]
has not been changed, the Torah law would require him to destroy the
entire building and return the beam to its owner.
Nevertheless, the Sages instituted a decree [to encourage] those who
repent; they ordained that all that is necessary is for him to return [the
beam’s] monetary value, and thus he will not forfeit his building.
Rabbenu Manoach asks: Since the mitzvah of sukkah is commanded by the Torah, and Torah law regards these boards as stolen, how can the Sages’ decree change their status in this context?
He explains that, as implied by the principle הפקר בית דין הפקר the Torah has granted the Sages the right to determine the status of property. Their decree can alter entirely a person’s rights to its title. Thus, in the present case, since Rabbinic law entitles the thief to use of the boards, he is permitted, according to Torah law, to use them as a Sukkah.
The Magen Avraham (637:5) writes that if the thief refuses to pay for the wood, it is considered to be the property of its original owner, and the thief does not fulfill his obligation.

This is a special leniency granted out of respect for the mitzvah of sukkah (Sukkah, ibid.). Since the thief has not made any changes in the wood itself or built a permanent structure from it, the Rabbinic decree mentioned above would not apply. Thus, during the rest of the year (and even in this case, after the Sukkot festival), the wood would have to be returned. During the festival, the Sages considered it to be the property of the thief and he is allowed to use without any constraints throughout the festival (Hilchot Gezeilah, ibid.).
Nevertheless, in his Kessef Mishneh and in his Shulchan Aruch (Orach Chayim 637:3) Rav Yosef Karo gives two examples of a stolen sukkah which one is forbidden to use a sukkah that had been constructed on a ship or one that had been constructed or a wagon. Since the thief did not build anything, the abovementioned Rabbinic decree does not apply; nor are they affixed to land, and hence the principle that landed property cannot be stolen is not relevant.

Though the Jewish inhabitants of the city would surely not object to use of public property for this purpose, the gentile inhabitants of the city would. Since they also have a share in this property, building a sukkah there is equivalent to stealing from the public (Magen Avraham 637:3).
Nevertheless, since the theft of land is involved...

for the reasons mentioned above. Note the Magen Avraham, ibid. and the Bi’ur Halachah, who discuss whether or not it is permitted to recite a blessing when using such a sukkah.