1) Yes, we have a majority of solid walls because the walls on each side are considered as 4 solid Amos.

2)

a. Since on each side there are 3 solid Amos and only one Amah break, this means we have a majority of solid for the walls on each side. When the solid wall is greater than the air in between we do not say "Asi Avira d'Hai Gisa..." (see Shulchan Aruch OC 363:34).

b. The Mishnah Berurah (OC 363:145) explains when "Asi Avira..." applies and when it does not apply. The discussion in the Shulchan Aruch there involves a Mavuy with an opening of 20 Amos wide, which we try to partially fill up, leaving a space of 2 Amos from the wall, and then having a solid pillar of 3 Amos. We do the same thing on the other side of the opening to the Mavuy, so we end up with 2 open Amos and 3 closed Amos. Because the closed part is greater than the open part on each side, we say "Omed Merubah..." and we have 5 closed Amos on each side. This is a total of 10 Amos, and since the open part of the Mavuy is 10 Amos, we have "Omed k'Kerubeh." "Omed k'Merubeh" means that the solid is equal to the open, and this is sufficient to consider the entire space as closed.

The question is, why do we need 2 open Amos and 3 closed Amos on each side? Since we usually say that if the closed is equal to the open, this is considered as closed. It should follow that it should suffice to have 2 1/2 closed Amos and 2 1/2 open Amos on each side!

The answer is that this scenario is weaker than the usual set-up because it is breached on both sides of the entrance to the Mavuy. If both sides are breached, then if the open is equal to the closed we say "Asi Avira...." In order not to say "Asi Avira..." we require that the closed be more than the open on both sides of the Mavuy.

3)

a. See Tosfos to Sukah 17a (fourth line from the top of the page) who says that "Asi Avira d'Hai Gisa..." does not apply in a scenario where Lavud is being applied, because when one applies Lavud, this means that the wall is totally solid. See Aruch ha'Shulchan (OC 363:53) who says that since Lavud is a Halachah l'Moshe mi'Sinai, "Asi Avira..." does not apply to override the Halachah l'Moshe mi'Sinai.

b. After looking more into the question of which of the 2 rules -- Lavud or Asi Avira -- take precedence over the other, I have found that it is not so simple and there seem to be contradictions between different sources:

(1) The first source is from a different area of Halachah, the laws of Tzitzis. The Magen Avraham (beginning of OC 16) cites the Maharil who says that one should make the shoulders of the Arba Kanfos garment wide, because otherwise there will be a problem of "Asi Avira d'Hai Gisa ud'Hai Gisa u'Mevatel Lei"; the air on each side of the shoulder "strap" will cancel out the "strap."

(2) The Sha'arei Teshuvah there (16:1, printed on the page with the Mishnah Berurah) cites the She'elas Ya'avetz 1:20 (of Rav Yakov Emden) who writes that "Asi Avira..." is not an appropriate term here. The Ya'avetz writes that "Asi Avira" applies only when one has air which is transformed by Lavud to become a Mechitzah, but not for an item of clothing. Since the clothing is solid, and does not require any air to be joined up with it, "Asi Avira" does not have the power to cancel out a solid item of clothing.

(3) The Machatzis ha'Shekel, on the above Magen Avraham, writes that the term "Asi Avira" used by the Maharil is in fact a borrowed phrase, because "Asi Avira" can work only to cancel out air which has been considered Halachically solid. "Asi Avira" cannot cancel out a solid item of clothing. The Machatzis ha'Shekel seems to agree with the argument of the Ya'avetz, and therefore he wrote that "Asi Avira" cannot be taken literally. The Mishnah Berurah (16:1) also appears to agree with the Ya'avetz and Machatzis ha'Shekel, because he writes that one should make the shoulder pieces of the Talis broad so that they should be easily recognizable and should be considered an item of clothing, and not merely straps. We see that the Mishnah Berurah does not mention the words "Asi Avira..." which suggests that he agrees that "Asi Avira" is a borrowed phrase as far as Tzitzis is concerned.

We do, however, observe in the words of the Ya'avetz that against air transformed by Lavud to become a Mechitzah it is appropriate to say "Asi Avira." This would seem to contradict Tosfos and the Aruch ha'Shulchan that I cited earlier, who says that "Asi Avira" cannot override Lavud.

I do not know how much time I will have to try to resolve this contradiction, but at least we have seen that there is a problem, and I hope I will be able to sort it out, bs'd.

4) The Mishnah in Eruvin 16b states that one may make a Mechitzah out of 3 ropes, each one on top of the one below it, with slightly less than 3 Tefachim between each rope. The combined width of the ropes is slightly over a Tefach thick. The first rope is slightly less than 3 Tefachim above the ground. Therefore, the air between the bottom rope and the ground is considered solid, through the law of Lavud. There is slightly less than 3 Tefachim between the first rope and the second rope, and, similarly, slightly less than 3 Tefachim between the second rope and the third rope. The air between the second and the third ropes is also considered solid, so the 3 "airspaces" possess a Din of slightly under 9 Tefachim. Since the combined thickness of the ropes is slightly over a Tefach, the combined height of the ropes and the airspaces is 10 Tefachim. 10 Tefachim represents a Mechitzah, and it does not matter what air is above the Mechitzah, because, as you pointed out, Moshe, it is not part of the Mechitzah. Once we have a Mechitzah of 10, this is quite sufficient for us.

Dovid Bloom

Here is a resolution of the contradiction, bs'd:

1) To attempt to answer the question I asked on the Ya'avetz in my previous reply, I am first going to pose another apparent contradiction between Tosfos in Sukah 17a, that I cited in my first reply, and a different Tosfos in Sukah, on 7a, DH Oseh.

2) The Gemara (Sukah 6b) states that a kosher Sukah must have two full walls, and then the third wall may be even just one Tefach. The Gemara (end of 6b) asks, where is this one Tefach of the third wall placed? The Gemara (7a) answers in the name of Rebbi Shimon that one makes a wall of a generous Tefach (Rashi writes that this means slightly more than a Tefach) and erects the wall less than three Tefachim away from one of the two full walls. Rashi explains that since the third wall is within three Tefachim of the full wall, we apply Lavud and the wall of "a Tefach and a bit" is now considered a wall of four Tefachim. Since the length of a full Sukah wall is a minimum of seven Tefachim, and since we now have a wall of four Tefachim, this means we have the majority of a full wall of a Sukah.

3) Tosfos (DH Oseh) asks, why do we need the third wall to be a Tefach long? Let the third wall be merely a thin pole! If the pole was less than three Tefachim away from the full wall, we could also say Lavud and the pole should now be considered a wall of a Tefach long! Tosfos answers, in his second answer at the end, that the airspace on the two sides of the pole would nullify the pole.

4) The Aruch la'Ner writes that he does not understand Tosfos. Surely, we only say "Asi Avira..." when there is an airspace of three Tefachim or more, so that Lavud is not applicable! If the airspace is less than three Tefachim, the Aruch la'Ner writes that we do not say "Asi Avira," as we find that if there is less than three Tefachim between the ropes, this represents a Mechitzah, or if poles are less than three Tefachim apart, this makes up a wall of a Sukah, even though there is airspace between one pole and the next. This must prove that we do not say "Asi Avira" to override Lavud! The Aruch la'Ner concludes that he saw in the Maharsha on Tosfos (17a) that he felt there is something difficult about Tosfos.

5) So let us look at the Maharsha there (17a). As we saw in my first reply, Tosfos writes there that "Asi Avira" cannot override Lavud. The Maharsha asks that this contradicts Tosfos on 7a. The Maharsha answers that there is a difference between the isolated pole of Tosfos on 7a, and a full wall created by more than one rope or pole. If it is more than an isolated pole, it is considered a full wall through Lavud, and the airspace cannot be Mevatel a full wall. If it is only an isolated pole, "Asi Avira" can override the pole.

6) I suggest that this solves the problem with the Ya'avetz. When the Ya'avetz wrote that "Asi Avira" can override Lavud, he was referring to a scenario where there is only one pole or rope involved, so the airspace is Mevatel it. If there are two or more ropes or poles, this is considered a full Mechitzah by virtue of Lavud, and "Asi Avira" cannot affect it.

Kol Tuv,

Dovid Bloom