PISKEI HALACHAH FROM R. ASHI REGARDING AN OVERLY TALL SUKAH
Items which would not normally be left out in the Sukah for seven days are not considered Batel to the Sukah and do not reduce its height (e.g. bedding), while items which are subject to Bitul (e.g. straw) will reduce the height (and certainly items which are normally assumed to be Batel e.g. dirt).
Question: What about straw which he does not intend to remove but he did not state his Bitul, or dirt which he placed without any special intent?
Answer: It is a Machlokes R. Yosi and Rabanan (taught regarding filling the open Tefach above a body to cause Tum'ah to rise above the enclosure).
Rabanan teach in the Mishnah that (only [Beraisa]) if one is Mevatel the straw or dirt it is Batel.
R. Yosi qualifies the Mishnah: (1) Straw which he does not intend to remove is deemed like dirt placed Stam and is Batel. (2) Also, if he intended to remove the dirt it is viewed like straw Stam and is not Batel.
If leaves droop down into the 20 Amos range, we check to see if those leaves would be sufficient to constitute Sechach on their own and they then validate the Sukah.
Regarding a Sukah whose leaves drop into the 10 Tefach (minimum) range there is a Machlokes.
(Abaye): We check for density (as above).
(Rava): It is not valid even without density, since these drooping leaves make the Sukah a miserable place.
A structure in part of the Sukah may be used to reduce the entire Sukah to (be considered) within 20 Amos.
This is providing that the structure has three walls.
This can be accomplished by building the structure along the entire far wall of the Sukah.
Alternately, if the structure is built along one of the side walls (in a Sukah with three walls) and the distance to the opposite wall is less than four Amos, with Dofen Akumah allowing us to use that wall.
Question: What is the Chidush of this alternate method?
Answer: To teach the rule of Dofen Akumah.
Question: But that is a Mishnah (17b permitting a Sukah-skylight if the walls are up to four Amos away from the edge of the skylight).
Answer: We might have thought to apply that Mishnah since the walls there are Kosher, but distant; whereas our wall is invalid (it is more than 20 Amos tall).
If the structure is in the middle of the Sukah we check to see that there are less than four Amos to the three walls.
Question: What is the news here?
Answer: Dofen Akumah.
Question: But we were just taught that Din!?
Answer: We might not have known to apply Dofen Akumah in multiple directions.
PISKEI HALACHAH OF RAV ASHI REGARDING AN OVERLY SHORT SUKAH
It is permitted to dig up the floor in the middle of the Sukah to raise its height to 10 Tefachim, providing the cavity is less than three Tefachim (Lavud) from the walls.
Question: Why don't we allow four Amos (Dofen Akumah)?
Answer: There we are taking advantage of an existing wall by bending it closer (Dofen Akumah) while here we are making the wall by extending it to 10 Tefachim (requiring Lavud).
GUD ASIK BY A SUKAH
If one builds a (7x7 Tefach) platform 10 Tefachim tall in a Sukah taller than 20 Amos (away from the walls, such that Dofen Akumah is not relevant):
(Abaye): We should apply Gud Asik to imagine the walls of this platform as extending upward to the Sechach.
(Rava): A Sukah cannot be built with imaginary walls.
If one erects four poles, placing a crossbeam from one to the other and places Sechach above them it is a Machlokes whether it is Kosher (R. Yakov) or Pasul (Chachamim).
(R. Huna): The Machlokes is when the poles are erected on the edge of a roof, where they argue over whether Gud Asik provides the walls for the Sukah (but all would invalidate such a structure in the middle of the roof).
(R. Nachman): Their Machlokes is when the structure is erected in the middle of the roof, since (according to R. Yakov) the poles provide a one-Tefach Mechitzah on each side [called Deyomdin] (while the Rabanan only allow a one-Tefach Mechitzah as the third Mechitzah of a Sukah).
Question: Does R. Nachman mean that all would agree that on the edge of the roof would be Kosher, or did he mean that there is a Machlokes here, as well (if the Chachamim require visible Mechitzos).
Question (on R. Huna): The Beraisa teaches that such a structure built on the ground (which should be the same as in the middle of the roof and yet) has the same Machlokes (meaning that R. Yakov permits without Gud Asik, relying on the poles as Mechitzos)!?
Answer: This indeed refutes R. Huna.
Question: Perhaps there is a second refutation of R. Huna?
We may infer from the cited Beraisa (that the Machlokes is when the structure is on the ground, equivalent to in the middle of the roof) that the edge of the roof is unanimously deemed Kesheirah.
This would refute the second point of R. Huna, as well.
Answer: It means that they argue in the middle of the roof in addition to their argument on the edge (and they discussed the case of the middle of the roof to indicate the degree to which R. Yakov permits employing the Deyomdin of the poles).
(Beraisa): If the poles of the structure are round, R. Yakov allows us to view them as though they were squared off and, if there would be a Tefach facing each direction, we apply the Diyumad principle (a Mechitzah made of a Tefach on each side).
The Chachamim require two proper Mechitzos while the third may be a Tefach.