1) MAKING A "KARPAF" FIT FOR CARRYING
OPINIONS: The Gemara suggests a number of ways to permit carrying inside a Karpaf larger than Beis Se'asayim. One of the ways is to build a new fence inside the Karpaf that is at least four Tefachim away from the old fence, with the express purpose of enclosing the Karpaf for residential purposes.
How long must this new fence be? Must it encircle the entire Karpaf, or does it suffice to run along only one full side (or a part of one side) of the Karpaf?
(a) The RITVA explains that the new fence must run along the full length of at least one side of the Karpaf in order for the entire Karpaf to be considered Hukaf l'Dirah. If the new fence is less than the length of the fence that it "replaces," it is ineffective; the area between it and the old fence is still usable, since the new fence does not separate it from the Karpaf by extending all the way to the ends of the old fence, and the old fence still serves to enclose the Karpaf (BI'UR HALACHAH OC 358:6).
(b) The ROSH (2:4) says that it suffices for the new fence to be longer than ten Amos, and it does not need to run along the full length of one side of the Karpaf. The Rosh bases his opinion on the Gemara earlier (24a) which says that carrying in a Karpaf becomes permitted merely by razing ten Amos of the old fence and rebuilding those ten Amos with intent to enclose the area for residential purposes. We see from there that erecting just ten Amos of a new fence suffices to make the Karpaf enclosed for residential purposes. (The Rosh understands that by building a new fence alongside ten Amos of the old fence, it is considered as though one has re-fenced that section. The area between the old fence and the new fence becomes a separate Karpaf entirely, which is joined to the first Karpaf by the gap between the end of the new fence and the end of the old fence.)
HALACHAH: The SHULCHAN ARUCH (OC 358:6) rules like the Rosh and says that as long as the new fence is longer than ten Amos, the Karpaf is considered Hukaf l'Dirah.
The BI'UR HALACHAH adds that the new fence must be built within ten Amos from the old fence. (This is consistent with the reasoning of the Rosh, who understands that the gap between the end of the new fence and the end of the old fence is an entranceway that joins two Karpafs with each other. If the gap would be wider than ten Amos, it would be considered a breach and not an entranceway, and the entire area would be viewed as one large Karpaf, and the new fence would be ignored.)
2) "PI TIKRAH YORED V'SOSEM"
OPINIONS: Rav and Shmuel argue whether the principle of "Pi Tikrah Yored v'Sosem" ("the edge of a roof-beam descends and encloses") applies to an awning that covers part of a valley (which is less than Beis Se'asayim in size). What exactly is the case?
(a) RASHI says that they argue only about a case in which there are four open sides to the awning (that is, it is merely a roof placed above four poles). If even one side would have a real Mechitzah, then both would agree that "Pi Tikrah Yored v'Sosem."
(b) TOSFOS in the name of RABEINU TAM explains that they argue about a case in which there are two or three Mechitzos. If there is only one Mechitzah, everyone agrees that we do not apply the principle of "Pi Tikrah Yored v'Sosem." If the awning has more than three Mechitzos (such as three and a half), everyone agrees that "Pi Tikrah Yored v'Sosem."
However, we may ask a fundamental question about the principle of "Pi Tikrah Yored v'Sosem." Whether we understand the argument as Rashi explains it or as Tosfos explains it, how is it ever possible to apply the rule of "Pi Tikrah Yored v'Sosem"? Since there is no Mechitzah on the side at which we view the roof-beam to descend and enclose the area, the area is exposed, and young goats are able to pass through it ("Gediyim Bok'in Bah")! Whenever there is a gap between the ground and a partition of more than three Tefachim, Gediyim Bok'in Bah prevents that area from being viewed as closed by a Mechitzah. Why, then, do we say that the edge of the roof-beam descends to form a Mechitzah, if there is a gap greater than three Tefachim below it?
The answer is that the principle of Gediyim Bok'in Bah does not invalidate a Mechitzah in every case of a three-Tefach gap. When a hanging Mechitzah is ten Tefachim high, and the normal law of Gud Achis is used to extend it to the ground, the principle of Gediyim Bok'in Bah prevents Gud Achis from extending the Mechitzah to the ground. However, when an area is covered (by an awning or other form of roof) and the law of "Pi Tikrah" is used, even though "Pi Tikrah" works through the same principle as Gud Achis, Gediyim Bok'in Bah does not prevent it from extending to the ground. (RITVA, 14a, 17b, 102a; see also KEHILOS YAKOV #3.)
The logical basis for this difference may be as follows. In order for a wall to be viewed as complete, it must serve not only as a wall, but it must serve as an indicator that a separate Reshus begins beyond it (that is, it must serve as a "Heker"). If a Mechitzah is raised more than three Tefachim from the ground, Gediyim Bok'in Bah invalidates it because it does not serve its purpose of indicating that the area inside is separate from the area outside. However, when a roof-beam is viewed to descend and form a Mechitzah, the roof itself serves to indicate that the entire area underneath it is separate from the area outside. Therefore, the presence of animals walking through the area does not invalidate the Halachic Mechitzah that "Pi Tikrah" creates. (M. KORNFELD)