GEMARA

Beraisa - R. Yakov: If one inserted four poles (in the surface of the roof) and put Sechach on them, the Sukah is Kosher;

Chachamim say, it is Pasul.

Rav Huna: They argue about when the poles are in the corners of the roof. R. Yakov says Gud Asik Mechitzta (we consider walls to extend upward. The walls of the house are considered walls for the Sukah); Chachamim do not say Gud Asik (therefore, the Sukah has no walls);

All agree that it is as if the poles are in the middle of the roof that the Sukah is Pasul.

Rav Nachman: They argue when the poles are in the middle of the roof.

Question: Does Rav Nachman mean that they argue only when the poles are in the middle, but all agree that it is Kosher when they are in the corners? Or, does he mean that they argue in both cases?

This question is not resolved.

Question (Beraisa - R. Yakov): If one inserted four poles in the ground and put Sechach on them, the Sukah is Kosher;

Chachamim Posel.

This is like in the middle of the roof (Gud Asik does not apply), yet they argue. This refutes Rav Huna.

Inference: They argue about poles in the ground, but all agree that if poles are in corners of the roof it is Kosher!

Suggestion: This refutes also Rav Huna's opinion that they argue about when poles are in the corners.

Rejection: Rav Huna can say that they argue in both cases. The Tana taught about poles in the ground to teach the extremity of R. Yakov's opinion, he is Machshir even when Gud Asik does not apply.

Beraisa - R. Yakov: If one inserted four poles in the ground and put Sechach on them:

If the poles are so thick that one could carve them out (and leave an 'L' - shape) and each side will be a Tefach, the poles are considered Deyumdim ('L' - shaped corner posts. Just like four Deyumdim around a well are considered like four walls to permit carrying inside, they are like four walls to Machshir a Sukah); if not, not.

R. Yakov holds that a Deyumad for Sukah must be a Tefach.

Chachamim say, two walls must be the proper size (seven Tefachim), the third can be (just more than) a Tefach.

RISHONIM

Ran (DH v'Garsinan): The Rif does not discuss a Sukah on top of poles. We are stringent to say that they argue even when the poles are in the corners; the Halachah follows Chachamim, who disqualify. Therefore, the Rif relied on what he says later, that a Sukah must have two proper walls and a third that is a Tefach.

Rambam (Hilchos Sukah 4:11): If one inserted a pole in each of four corners of the roof and put Sechach on them, since the Sukah goes to the edge of the roof, it is Kosher; we view the lower walls as if they go up to the edge of the Sechach.

Rebuttal (Ra'avad and R. Mano'ach): The Gemara did not resolve what Rav Nachman holds in this case. We must be stringent about a Safek mid'Oraisa

Defense (Rosh 1:6): Presumably, the Rambam had the text of Rav Shrirah Gaon, in which Rav Nachman explicitly says that if the poles are in the corners all agree that the Sukah is Kosher.

Rosh (ibid.): In all of our Seforim the Gemara does not resolve Rav Nachman's opinion, therefore we are stringent.

POSKIM

Shulchan Aruch (OC 630:6): If one inserted four poles, whether in the middle of the roof or in the corners, and put Sechach on top, the Sukah is Pasul.

Mishnah Berurah (29): Even though all agree that we say Gud Asik Mechitzta regarding Shabbos, regarding Sukah we require proper walls.

Question: The Rosh holds that mid'Oraisa, Tzuras ha'Pesach is considered a wall. If so, the Sukah should be Kosher even without Gud Asik!

Answer (Bi'ur Halachah DH No'etz): The Rosh allows Tzuras ha'Pesach only for the third wall.

Shulchan Aruch (ibid.): Some say that when the poles are in corners it is Kosher because we say Gud Asik Mechitzta.

Mishnah Berurah (30,31): Even regarding Shabbos we say Gud Asik only if the roof does not jut out past the walls of the house. Also, the Sukah must extend to the edge of the roof; all agree that we do not say Gud Asik and Lavud. One should not rely on this lenient opinion. (If there is no other Sukah available, he should eat in it without a Berachah - Sha'ar ha'Tziyon 39.)

Magen Avraham (8): Shiltei ha'Giborim says that we say Chokekim (if the poles are so wide that one could carve out the inside leaving two or three walls of the proper Shi'ur, it is considered as if there are such walls). The Halachah does not follow him.