Gemara

Question: Does the Heter to carry in the Mavoy include underneath the Korah?

Answer #1 (Rav, R. Chiya and R. Yochanan): One may carry under the Korah.

Answer #2 (Shmuel, R. Shimon bar Rebbi and Reish Lakish): One may not carry under it.

Suggestion: Those who permit hold that a Korah is for a Heker [for people outside the Mavoy.] Those who forbid consider a Korah like a Mechitzah. (Through Pi Tikra Yored v'Sosem, we extend the inner edge down to the ground. Under the Korah is outside the Mavoy.)

Rejection #1: All agree that a Korah is for a Heker. Those who permit hold that the Heker is for people outside. Those who forbid hold that the Heker is for people inside the Mavoy.

Rejection #2: All agree that a Korah is for a Mechitzah. Those who permit apply Pi Tikra Yored v'Sosem to the outer edge. Those who forbid apply it to the inner edge.

9a (R. Zakai - Beraisa): Bein ha'Lechayayim (the area parallel to the middle wall and even with the thickness of the Lechi), and under the Korah are both Karmelis.

R. Yochanan: Do not teach this in the Beis Medrash!

(Abaye): Presumably, R. Yochanan permits under the Korah, but he agrees that Bein ha'Lechayayim is forbidden.

(Rava): Also Bein ha'Lechayayim is permitted.

Support (Abaye, for himself - Rav): Bein ha'Lechayayim needs another Lechi [outside it] to permit it.

Suggestion: It is four by four. (It itself is a Karmelis!)

Rejection: Rav requires another Lechi to permit even if it is not four by four.

Rejection (Rava): That is when it is open to a Karmelis.

Inference: If it is open to Reshus ha'Rabim, it is permitted.

Objection: This is absurd! (Karmelis cannot be more stringent than Reshus ha'Rabim.)

Answer: It is reasonable. (Bein ha'Lechayayim would be a Karmelis if it were big enough.) When it opens to a Reshus (Karmelis) like itself, Matza Min Es Mino v'Ni'ur. (It joins with it to complete the Shi'ur.)

Shabbos 9a (Beraisa - Others): When the door is open, the threshold is like inside [the house, Reshus ha'Yachid]. When the door is closed, it is like outside (Reshus ha'Rabim).

(Rav): Others discuss the threshold of a Mavuy. Only the inner half is covered [by the Korah]. When the door is open, the threshold is like inside. (Rav permits carrying under the Korah.)

Rishonim

Rif (2b): We permit under the Korah or Bein ha'Lechayayim when it is open to Reshus ha'Rabim, but not if it is open to a Karmelis, even if it is not four by four, for Matza Min Es Mino v'Ni'ur.

Rebuttal (Ba'al ha'Ma'or): Under the Korah is permitted, but Bein ha'Lechayayim is forbidden, like Abaye. The Halachah follows Abaye in Ya'al Kagam (an acronym of six Halachos in which we rule like him against Rava. "Lamed" stands for a Lechi that came about by itself.) Abaye holds that a Lechi is a Mechitzah. Rava holds that it is for a Heker. Therefore, Bein ha'Lechayayim is forbidden even if it opens to Reshus ha'Rabim.

Defense (Milchamos Hash-m): The Rif is more reasonable. Rava learned from R. Yochanan, who permits a place less than four by four. If a Lechi were a Heker from the outside, its width would not matter! Also, in one version Abaye holds also a Korah is a Mechitzah, yet he permits under the Korah and forbids Bein ha'Lechayayim. Our Sugya says that all could hold that Korah is a Mechitzah, or that it is a Heker, and even so they argue about under the Korah. Rather, Abaye holds that a Korah has more Heker than a Lechi on its outer edge. Perhaps this is because a Korah must be a Tefach wide. A Lechi can be thin like a thread, so its outer edge is not recognized. Therefore, Bein ha'Lechayayim is forbidden even if the Lechi is thick. Rava holds that in both cases the outer edge is Nikar. In the Sugya of a Lechi that came about by itself, some texts say that Abaye holds that a Lechi is a Mechitzah, and Rava holds that it is a Heker. This is correct; R. Chananel says so. Many explain our Sugya oppositely. We should not explain the Heter of Bein ha'Lechayayim in a way that opposes Rava, for the Halachah always follows him. Rather, we rely on versions which say that the outer edge of the Lechi seals [the opening]. However, why does the Rif permit Bein ha'Lechayayim that opens to Reshus ha'Rabim even if it is four by four? It seems that he holds that Rava holds that a Lechi is a Heker, or the outer edge seals. This is even if Bein ha'Lechayayim is four by four.

Rambam (Hilchos Shabbos 17:11): One may carry in a Mavoy under the Korah, or Bein ha'Lechayayim. This is if it was next to Reshus ha'Rabim. If it was next to Karmelis, one must make another Lechi to permit the opening, for Matza Min Es Mino v'Ni'ur.

Rebuttal (Ra'avad): Under the Korah is always permitted. Rava distinguishes between next to Reshus ha'Rabim and next to Karmelis only regarding Bein ha'Lechayayim. The Rambam rules like Rava. Some forbid Bein ha'Lechayayim, like Abaye.

Rosh (1:10): The Halachah is, one may carry in a Mavoy under the Korah, or Bein ha'Lechayayim, like Rava. This is if it was next to Reshus ha'Rabim, but not if it was next to Karmelis, for it joins with a similar Reshus. The Rambam equated under the Korah with Bein ha'Lechayayim. He forbids both when they are open to Karmelis. The Ra'avad permits under the Korah even when it is open to Karmelis. The Rif connotes like this. Rava brought a proof only for Bein ha'Lechayayim. He did not need to bring a proof for under the Korah. He holds that a Korah is for a Heker (12b), so surely one may carry under it. The Gemara permits under the Korah if it is for a Heker, but not if it is a Mechitzah. The Gemara later said that they could argue even if all agree that a Korah is for a Heker, or all agree that it is a Mechitzah. However, we see that the Gemara held like it initially suggested. Therefore, since Rava holds that Korah is for a Heker and Lechi is for a Mechitzah, under the Korah is permitted. He permits Bein ha'Lechayayim only when it opens to Reshus ha'Rabim, for then Bein ha'Lechayayim is Batel to the Mavoy. However, some texts say that Rabah holds that a Lechi is a Mechitzah, and Rava holds that it is a Heker. If so, it is like a Korah. The Ba'al ha'Ma'or's proof is invalid. Perhaps the outer edge seals! The Ri proved that the one who forbids Bein ha'Lechayayim does not forbid because it is a Mechitzah, rather, for he holds that the inner edge seals.

Rosh (Shabbos 1:17): Rav holds that the Korah permits carrying in the threshold. If it were permitted by a Lechi it would be forbidden, for its inner edge is like a Mechitzah that permits only inside it. A Korah permits because it is a Heker.

Poskim

Shulchan Aruch (OC 365:4): One may carry in a Mavoy under the Korah, or Bein ha'Lechayayim.

Mishnah Berurah (25): Some Poskim hold that this is only if Bein ha'Lechayayim is less than four by four. Then, it is Batel to the inside, and one may carry there or take from there to inside. However, if it is four by four, it is a Karmelis to forbid carrying there more than four Amos, or to transfer from there to Reshus ha'Rabim or Reshus ha'Yachid. Some Poskim do not distinguish, and permit even if it is four by four.

Kaf ha'Chayim (39): Tosfos (9a DH l'Raban), the Ritva and Ba'al ha'Ma'or forbid if it is four by four. The Ramban permits, and it seems that the Rashba agrees.

Shulchan Aruch (ibid.): This is if it is open to Reshus ha'Rabim. If it is open to Karmelis, both of them are forbidden, for it joins to the Karmelis, for Matza Min Es Mino v'Ni'ur.

Beis Yosef (DH Mutar): The Magid Mishneh says that the Rif holds like the Rambam. Since the Rosh and Rambam agree, and perhaps the Rif agrees, we follow them.

Mishnah Berurah (27): Eliyahu Rabah and Even ha'Ozer are lenient to permit under the Korah even if it is open to Karmelis. Especially if it is four wide and strong enough to hold plaster, surely it is permitted even if it is open to Karmelis, for Pi Tikra Yored v'Sosem, so it is considered a Mechitzah.

Bi'ur Halachah (DH Bein): Also Rashi, Tosfos the Rosh and Milchamos Hash-m in Shabbos holds like the Ra'avad.

Kaf ha'Chayim (42): The Rema did not comment. This shows that he agrees with the Mechaber. Also the Bach, Levush and R. Zalman hold like this.

Bi'ur Halachah (DH b'Patu'ach): When it opens to Reshus ha'Rabim, it is permitted even if the Mavoy has a door, and it is locked, and the Lechi is outside the door. It does not matter whether or not there is a platform three tall.