Question: If a four-Tefach plank always invalidates a Sukah, then why does R. Meir, in the Beraisa, allow Sechach when there is an equal amount of space as the Pasul boards between each board?!

Answer (R. Huna bar R. Yehoshua): That Sukah has a unique configuration which allows for an eight-Tefach Kosher Sukah in the middle.

The alternating board-open, board-open takes place three times from each side of an eight-Amah-wide Sukah (the 'open' from each side meet in the middle).

The boards are, indeed, Sechach Pasul, but they are within the four Amos limit for Dofen Akumah, leaving an eight Tefach Kosher Sukah.

(Abaye): If one diminishes a three Tefachim open space (with either Kosher or non-Kosher Sechach) in a Sukah larger than the minimum, the Sukah is Kosher.

There is neither the Shiur of space nor that of Sechach Pasul to invalidate it.

If one did the same thing in a minimum Sukah it would be Pasul, because it does not have the Shiur Sechach for a Sukah.

If one filled in part of the space with canes, the minimum Sukah is Kosher, because of the principle of Lavud.

The above applies when the open space is next to the wall.

R. Acha and Ravina argue what the Din will be in the middle of the Sukah.

(Ravina): We would apply Lavud in the middle of the Sukah, as well.

(R. Acha): Lavud is applied only next to a wall.

Question: What is the rationale for Ravina?

Answer: He applies the leniency found by the Koreh of a Mavoy.

To carry in a Mavoy requires (either a Lechi at the entrance or) a Koreh across the entrance of the Mavoy.

If the beam is interrupted in its middle by a space of up to three Tefachim, it is a valid Koreh (Lavud).

Question: Why, then, would R. Acha not allow Lavud in the middle?

Answer: This is restricted to the beams of a Mavoy, whose application is mid'Rabanan, as we see in the Beraisa where, when dealing with Tum'ah d'Oraisa, Lavud does not 'close up' a small skylight.

Question: How will Ravina understand this Beraisa?

Answer: Hilchos Tum'ah have unique specifications (the Halachah l'Moshe mi'Sinai is that regarding Tum'ah, there is no Lavud in the middle).

(R. Yehudah b. Ilai): A skylight covered with Sechach is Kosher.

(R. Yishmael b'Rebbi Yosi): My father taught that this only applies up to four Amos from the walls (Dofen Akumah).

(R. Yehudah b. Ilai): A type of small fish called Abruma is permitted.

(R. Yishmael b'Rebbi Yosi): My father taught that its Kashrus depends on which river it is drawn from (some rivers grow insects, etc).

(Abaye): A type of small fish called Tzachnasa from the River Bav is permitted.

Question: Why are we not concerned that this small fish will be interchanged with Tameh fish?

Answer: Because the Bav is a swift-flowing river and non-Kosher fish, which have no spinal cord, could not survive in it.

Question: But we find non-Kosher fish in other swift-flowing rivers!?

Answer: It is because the waters of the Bav are very salty and non-Kosher fish, which have no scales, could not survive in it.

Question: But we find non-Kosher fish in salty waters!?

Answer: It is because the mud on its river-bed is inhospitable to insects, and non-Kosher fish.

(Ravina): Fish from the Bav are now no longer permitted because the waters of other rivers, which bring insects with them, flow into it.

The walls of a Sukah may be made by uprights placed less than three Tefachim apart (Lavud).

This is taught regarding the case in the Mishnah of three walls created by the houses facing into the courtyard.

There we learned that if the overhanging roof extends more than four Amos into the courtyard, the house walls cannot serve as the walls of the Sukah, and it does not suffice to put Sechach over the open area beyond the overhang.

(Abaye): The Sukah is allowed even without the uprights, as we apply Pi Tikrah Yored ve'Sosem to create inner walls from the ceilings which surround the courtyard.

(Rava): We do not apply Pi Tikrah Yored ve'Sosem in this case.

Question (Rava): If Pi Tikrah indeed creates walls then it should create a wall and close the third wall of a Sukah, as well (where we only have two parallel walls and boards for Sechach between them)!?

Answer (Abaye): Abaye concedes that Pi Tikrah Yored does not apply in such a Sukah, as the Rabanan forbade it because it resembles an open Mavoy.

Question: Shall we suggest that Rava and Abaye are arguing in the Machlokes Rav and Shmuel?

(Rav): It is permitted to carry on Shabbos inside an Achsadra that is not near a house because Pi Tikrah Yored ve'Sosem (even by all walls).

(Shmuel): One may not carry beyond four Amos.

Abaye who permits an Achsadra without uprights seems to be like Rav, while Rava is like Shmuel who does not say Pi Tikrah on four sides (only on three).

Answer: There is no Machlokes Abaye and Rava within the view of Shmuel, and even Rava will agree that Shmuel will forbid our Achsadra without uprights.

The Machlokes Abaye and Rava is regarding the opinion of Rav.

Abaye permits the Sukah according to Rav.

Rava (who concedes that a field-Achsadra allows for Pi Tikrah) holds that the allowance there is because the roof (and, by extension, the Gud Achis walls) were made for the sake of a Sukah.

But by the Sukah in the courtyard, the overhangs were not made for the Sukah, and Pi Tikrah will thus not apply.