GEMARA

6b - Beraisa: If a Sukah has two walls k'Hilchasan, the third wall can be just a Tefach (this is a tradition from Sinai).

7a - R. Simon or R. Yehoshua ben Levi: The short wall must be a Tefach Sochek. One puts it within three Tefachim of the end of one of the other walls; it is considered Lavud.

Rav Yehudah: A Sukah like a Mavoy is Kosher. The Tefach wall can be at any exit;

R. Simon or R. Yehoshua ben Levi: The short wall must be more than four Tefachim. He puts it within three Tefachim of one of the other walls; it is considered Lavud.

Version #1 (Rava): It is permitted only through Tzuras ha'Pesach.

Version #2 (Rava): Alternatively, it is permitted through Tzuras ha'Pesach.

Version #3 (Rava): Additionally, it needs Tzuras ha'Pesach.

Rava: The same applies to Shabbos. Migo (since) it is a wall regarding Sukah, it is a wall regarding (carrying on) Shabbos.

Question (Abaye): We do not say such a Migo!

(Beraisa): A Sukah wall is like a wall for Shabbos, provided that there are not three Tefachim between poles. There is a stringency of Shabbos over Sukah. A Mechitzah is valid for Shabbos only if the Omed Merubah Al ha'Parutz (the width of the wall that stands exceeds the gaps); this does not apply to Sukah.

Suggestion: This teaches that (even) on Shabbos of Sukos) we are more stringent regarding Shabbos than regarding Sukah. We do not say that since it is a wall regarding Sukah, it is a wall regarding Shabbos!

Answer (Rava): No, it teaches that we are more stringent regarding any other Shabbos than regarding Shabbos of Sukos.

Question: If so, the Beraisa should also teach that there is a stringency of other days of Sukos over Shabbos of Sukos! On other days we require a Tefach Sochek (for the third wall), but a Lechi (vertical post of any width) suffices for Shabbos of Sukos! You yourself say that if one put Sechach over a Mavoy with a Lechi, it is Kosher (the Lechi is considered like a wall)!

Answer (Rava): The Tana did not need to teach that. He taught that Migo applies from something lenient (Sukah) to something stringent (Shabbos), all the more so Migo applies from stringent to lenient!

RISHONIM

Rambam (Hilchos Sukah 4:12): If a Sukah has many openings and gaps in the walls it is Kosher. This is even if Parutz Merubah Al ha'Omed. However, if there is a gap of more than 10 Amos, then the Parutz cannot exceed the Omed.

Magid Mishnah: The Rambam learns from the Beraisa which requires Omed Merubah Al ha'Parutz for Shabbos, but not for Sukah. The Rambam permits Parutz Merubah only regarding the third wall of the Sukah. The Rambam forbids this regarding Shabbos even when there is Tzuras ha'Pesach.

Question (Lechem Mishneh): The Gemara says that there is a stringency of Mechitzos Shabbos over Mechitzos Sukah, i.e. Shabbos requires Omed Merubah Al ha'Parutz. The Magid Mishnah allows Parutz Merubah only for the third Sukah wall. Such a wall is Kosher also for the third wall regarding Shabbos if it has Tzuras ha'Pesach, which the Rambam (4:2) requires for the third wall of Sukah!

Suggestion: Perhaps this leniency of the third wall is only if the two full walls meet, but not if they are parallel.

Rejection: We are more lenient about when the two walls meet than when they are parallel.

Answer (Lechem Mishneh): Perhaps we are more stringent about a Chatzer regarding Shabbos than we are about Sukah. We find that a Chatzer is more stringent than a Mavoy regarding an opening of more than 10 Amos (a Chatzer needs a plank four Tefachim wide, whereas a Mavoy needs only a Lechi and Korah).

Chazon Ish (OC 75:5): The Beis Yosef explains that Rashi and the Rosh explain that the Beraisa discusses Omed Merubah in all the walls together. Presumably, the Magid Mishnah disagrees, for otherwise he would have explained the Rambam similarly.

Question (R. Mano'ach): Our Gemara was unable to prove that Parutz Merubah Al ha'Omed is Kosher for Sukah. It is Machshir only when they are equal!

Answer (R. Mano'ach): In Eruvin the Gemara allows Parutz k'Omed regarding Shabbos. Sukah is more lenient, therefore even Parutz Merubah is permitted.

Note: Clearly, Parutz Merubah Al ha'Omed is allowed for the third wall, since even a Tefach suffices! R. Mano'ach must understand that the Rambam allows Parutz Merubah Al ha'Omed for all sides. Rashi (7a DH Mah) allows Parutz Merubah for all the sides combined.

Rosh (7): The Rif omits Rava's teaching that a wall of a Sukah is considered a wall for Shabbos. This is because he holds that even when the Sukah is like a Mavoy, Tzuras ha'Pesach is required, and this is a proper wall for Shabbos.

Note: The Rif (3a) does bring that a wall regarding Shabbos is a considered a wall regarding Sukah.

Question: According to the versions that Rava requires Tzuras ha'Pesach even for a Sukah like a Mavoy, why is the Migo needed?

Answer (Ran DH Garsinan): There are other cases in which a wall is Kosher mid'Oraisa for Sukah but not for (a regular) Shabbos, e.g. Parutz Merubah Al ha'Omed. Further, mid'Rabanan one may not carry on Shabbos unless there is a plank or Lechi or Korah on the fourth side. The Migo allows carrying in a Sukah of three walls. The Rif did not bring Rava's Migo. Some say that the Rif holds that the Migo makes a Reshus ha'Yachid mid'Oraisa to Mechayev one who throws from Reshus ha'Rabim into the Sukah, but mid'Rabanan it does not permit to carry inside. This does not seem correct, but one should be stringent.

Question: Why don't we say the Migo to be stringent, i.e. just like it is not a wall for Shabbos, it is not a wall for Sukah?

Answer #1 (brought in Ran DH v'Amar (1)): Some say that the Migo is only for mid'Rabanan laws, i.e. it is a reason not to decree.

Answer #2 (Ran ibid.): When the Torah allows a wall for Sukah (e.g. Parutz Merubah), surely it allows it for all seven days, which includes Shabbos.

POSKIM

Tur (OC 630): ...One puts a Tefach Sochek within three Tefachim of a wall and stands up a beam even with the end of the other wall, and puts a beam on top. The Sukah is Kosher, and one may carry in the Sukah even on Shabbos. Just like the Tefach is considered a wall regarding Sukah, it is a considered a wall regarding Shabbos.

Beis Yosef (DH u'Mah she'Chasav u'Mutar): Since the tradition from Sinai teaches that the Tefach is like a full wall of a Sukah, it is a considered a wall regarding Shabbos of Sukos.

Question: Since the Tur requires Tzuras ha'Pesach, why did he need to teach the Migo? Tzuras ha'Pesach is always a Mechitzah for Shabbos!

Answer (Beis Yosef DH v'Hashta): Normally, three Mechitzos make a Reshus ha'Yachid mid'Oraisa, but mid'Rabanan one may not carry inside without a plank or Lechi on the fourth side. The Tur teaches that on Shabbos of Sukos it is permitted to carry even mid'Rabanan. Since the walls help for Sukah, they help for Shabbos.

R. Chaim ha'Levi (Al ha'Rambam Shabbos 16:16): Even when Tzuras ha'Pesach permits, it is not a Mechitzah. Rather, a gap of more than 10 Amos is a Pirtzah that invalidates a Mechitzah. Tzuras ha'Pesach causes the opening to be a Pesach (entranceway), which does not invalidate. However, if Parutz Merubah, even though there is no Pirtzah, there is no Mechitzah.

Mishnah Berurah (OC 630:11): After making the third wall in a Kosher way one may carry in the Sukah on Shabbos and transfer through a window from the house to the Sukah. Even though on other Shabbosos we require some Tikun on the fourth side, on Shabbos of Sukos since it is a wall regarding Sukah, it is a wall regarding Shabbos. One should be stringent unless he is in pressed circumstances.