1) THE ENACTMENTS OF A "KORAH" AND "SHITUF" FOR A "MAVOY"
QUESTION: The Mishnah states that "a Sukah which is taller than 20 Amos is Pasul." The Gemara quotes a similar Mishnah at the beginning of Eruvin (2a) that says that a "Mavoy which is taller than 20 Amos should be lowered." The Gemara asks why the Mishnah here says merely that the Sukah is Pasul and does not teach how to rectify the problem, while the Mishnah in Eruvin teaches how to rectify the problem.
RASHI (DH Mavoy) explains the Mishnah in Eruvin. The Rabanan required that a Mavoy, a three-sided alleyway that opens into Reshus ha'Rabim, must have a Korah (beam) across the top of the open side in order to permit carrying inside the Mavoy. Since a three-sided alleyway resembles a Reshus ha'Rabim, a public domain, the Rabanan prohibited carrying more than four Amos there (lest people think that they may carry in a real Reshus ha'Rabim) unless there is a Korah at the opening to Reshus ha'Rabim. The Korah reminds people that it is not a Reshus ha'Rabim.
Rashi adds that the Rabanan made an additional enactment of "Shituf Mavoy." He explains that in the times of the Gemara, Chatzeros opened into a Mavoy. The people who lived in each Chatzer were the joint owners of that Chatzer. The Mavoy, in turn, was owned by all of the residents of the Chatzeros. The Rabanan prohibited carrying from a private Reshus ha'Yachid (Chatzer) to a less private Reshus ha'Yachid (Mavoy). (Similarly, they prohibited carrying from one's home, a private Reshus ha'Yachid, to the Chatzer, a less private Reshus ha'Yachid, unless an Eruv Chatzeros is made.) In order to permit carrying from the Chatzeros into the Mavoy, a "Shituf" must be made. The Shituf joins together all of the members of the Chatzeros and effectively gives them all equal rights to use the Mavoy, as if the Mavoy had only one owner.
Why does Rashi mention the enactment of Shituf? It is irrelevant to the Gemara's discussion of the enactment of the Korah, which permits carrying in the Mavoy itself. The Shituf is an auxiliary enactment which permits carrying from the Chatzeros to the Mavoy, once there is already a Korah in the Mavoy. In what way is Shituf related to the Gemara's discussion of how to rectify the height of the Mavoy by lowering the Korah? (MAHARAM)
ANSWER: Perhaps Rashi mentions Shituf in order to explain why the enactment of Korah was made for a Mavoy.
Rashi writes that the reason why a Mavoy needs a Korah is in order that people not mistakenly think that just as they are permitted to carry in a Mavoy, they are permitted to carry in a real Reshus ha'Rabim. Rashi could have written another reason for why a Mavoy needs a Korah: in order to prevent people from carrying from there into Reshus ha'Rabim through its open side. Rashi, however, writes instead that the Mavoy itself resembles a Reshus ha'Rabim and thus people might err and think that if they may carry in the Mavoy, they may also carry in Reshus ha'Rabim.
How does Rashi know that the enactment of a Korah is because a Mavoy resembles a Reshus ha'Rabim, and not because of the fear that people might carry from the Mavoy into Reshus ha'Rabim?
Without a Korah, one is permitted to carry an object in a Mavoy within a distance of four Amos. If the purpose of the Gezeirah against carrying in a Mavoy (without a Korah) is to prevent people from carrying from the Mavoy into Reshus ha'Rabim, then the Gezeirah should also prohibit moving an object any distance in a Mavoy, lest one stand at the exit of the Mavoy, less than four Amos from Reshus ha'Rabim, and carry an object less than four Amos into Reshus ha'Rabim. It must be that the Rabanan's only concern was that one might think that if he is permitted to carry in a Mavoy he is also permitted to carry in a Reshus ha'Rabim. Accordingly, there are no grounds to limit the prohibition of carrying to less than four Amos.
In what way, though, is a Mavoy similar to Reshus ha'Rabim? Rashi explains that a Mavoy is similar to a Reshus ha'Rabim in that it is a publicly-owned domain outside of a number of privately-owned domains. This is evidenced by the requirement for Shituf. The requirement for Shituf shows that it is a non-privately owned domain outside of private domains, and in that way it resembles a Reshus ha'Rabim and thus requires a Korah. This explains why Rashi discusses Shituf -- it is an introduction to why a Korah is needed. (M. KORNFELD)
2) THE MISHNAH'S USAGE OF THE WORD "PASUL"
QUESTION: The Gemara asks why the Mishnah here says that "a Sukah which is taller than 20 Amos is Pasul" and does not teach how to rectify the problem, while a similar Mishnah in Eruvin (2a) teaches how to rectify the problem: "a Mavoy which is taller than 20 Amos should be lowered."
The Gemara (in its first answer) says that the reason why the Mishnah teaches that a Sukah is Pasul is because the requirement that the height of a Sukah be less than 20 Amos is mid'Oraisa. In contrast, the Mishnah in Eruvin teaches how to correct a Mavoy which is too high, because the requirement for a Mavoy to have a Korah below 20 Amos is mid'Rabanan.
How does this difference affect whether the Mishnah says "Pasul" or whether it teaches how to rectify the problem?
RASHI explains that when the Gemara says that the Pesul is mid'Oraisa, it means that the Pesul existed before the Mishnah was taught, and therefore it is appropriate to say "Pasul." When, however, the Pesul is only mid'Rabanan, such as the Pesul of a Mavoy which has a Korah higher than 20 Amos, it is not possible for the Mishnah to say that it is "Pasul," because the Pesul was not known before the Mishnah was taught.
What exactly does Rashi mean? Why can the Mishnah not teach the Pesul d'Rabanan by saying that a Mavoy taller than 20 Amos is "Pasul"? Although it is true that this is the first time that the Pesul is taught, why is the word "Pasul" inappropriate in such a case?
ANSWER: Rashi means that the proper method to teach a Takanah or obligation is to teach first the positive (that is, to teach first what is required), and then to teach the negative (what is invalid). Thus, the Mishnah can begin with the word "Pasul" (the negative aspect of the law) only if the positive aspect, of what is required, has already been taught. The Torah already teaches that there is a requirement to build a Sukah. Therefore, it is possible for the Mishnah to add that a certain detail will invalidate the Sukah. In contrast, the prohibition to carry in a Mavoy without a Korah (as well as any other rabbinical enactment) is not taught in the Torah; it appears for the first time in the Mishnah. Therefore, the Mishnah cannot begin with "Pasul," but must begin with "Yema'et," which includes both the positive ("keep it lower than 20 Amos") as well as the negative ("do not raise it above 20 Amos").

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3) HALACHAH: A SUKAH TALLER THAN 20 AMOS
OPINIONS: The Gemara presents four opinions for why a Sukah taller than 20 Amos is Pasul. There are practical differences between these opinions with regard to whether there are exceptions to the Pesul of a Sukah taller than 20 Amos, and under what circumstances those exceptions apply.
1. Rabah (2a) says that the reason for why a 20-Amah-tall Sukah is Pasul is because the Sechach is not readily noticeable. According to this reason, if the walls of the Sukah reach all the way up to the Sechach, then a person's eye follows the walls and notices the Sechach, and thus the Sukah is valid even if it is taller than 20 Amos.
2. Rebbi Zeira says that it is Pasul because the Sechach does not provide shade to the lower part of the Sukah when it is so high. According to this reason, if the length and width of the Sukah are at least four by four Amos, then the Sechach does provide shade even though it is higher than 20 Amos, and such a Sukah is valid.
3. Rava says that a Sukah taller than 20 Amos is Pasul because the Torah requires that the Sukah be a "Diras Arai," a temporary dwelling. A structure taller than 20 Amos is normally built as a "Diras Keva," a permanent dwelling. A Sukah cannot be built in the manner of the type of building that is a "Diras Keva." According to Rava, no Sukah taller than 20 Amos can be valid.
4. The Gemara (2b) cites a fourth opinion. Rav Chanan bar Rabah says that a 20-Amah-tall Sukah is Pasul only when it is so narrow that it "contains only his head, most of his body, and his table," which is defined as seven Tefachim long by seven Tefachim wide. (TOSFOS explains that such a small structure is considered a chicken coop and is not called a dwelling place.) If, however, the length and width of the Sukah are larger than seven by seven Tefachim, the Sukah is valid even if it is taller than 20 Amos.
Which opinion does the Halachah follow?
(a) RABEINU CHANANEL says that the Halachah should follow the view of Rabah. His reasoning (as cited by the Rif) is that Rabah was an expert in Rav's teachings and knew best what Rav taught. If Rabah stated that a tall Sukah is valid when its walls reach the Sechach, then he must have known that this is what Rav taught. Since Rav was a very early Amora, the Halachah should follow his view. (This is how the KORBAN NESANEL understands the intention of Rabeinu Chananel.)
The Halachah certainly should not follow Rava, because when the Amora'im (Rav Yoshiyah, Rav Huna, and Rav Chanan bar Rabah) quote Rav, none of the statements they quote in his name is consistent with Rava's opinion. The RA'AVAD and BA'AL HA'ITUR add that Rava was a student of Rabah, and thus the Halachah should follow the teacher, not the student.
(b) However, the ROSH points out that the RIF rules in accordance with Rava. The Rosh explains the Rif's reasoning as follows. First, of all the Amora'im quoted in the Gemara, Rava is the latest ("Basra"), and the Halachah normally follows the latest opinion (even though he was a Talmid of Rabah). Second, later in the Gemara (7b) Abaye records a list of Tana'im who maintain that a Sukah is a "Diras Keva," and he includes Rebbi Yehudah of the Mishnah. This implies that the Rabanan and most other Tana'im maintain that a Sukah is not a "Diras Keva," and that any Tana who maintains that it is a "Diras Keva" is expressing the opinion of a minority. According to all of the Amora'im other than Rava, the Rabanan of the Mishnah do permit a Sukah over 20 Amos tall even though such a structure is a "Diras Keva." Hence, it is evident from Abaye that the Halachah should follow Rava, who says that a structure that is fit to be a "Diras Keva" should never be a valid Sukah.
According to Rava, the Mishnah is more precise. The Mishnah makes no mention of any exceptions to the Halachah that a Sukah 20 Amos tall is Pasul, as Rava maintains. This is the ruling of the SHULCHAN ARUCH (OC 633:1).

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