1) HALACHAH: MAKING AN ACQUISITION ON SHABBOS
OPINIONS: Beis Shamai and Beis Hillel argue whether one may be Mevatel his Reshus on Shabbos to permit the other residents of the Chatzer to carry, or whether one may be Mevatel his Reshus only before Shabbos. Abaye explains that according to Beis Shamai, Bitul Reshus is an act of giving ownership (an act of Kinyan) of one's share in the Chatzer to the other residents, and an act of giving ownership (Kinyan) is prohibited on Shabbos. Beis Hillel disagrees and maintains that Bitul Reshus is not an act of giving ownership, but rather it is an act of withdrawing one's ownership, which one may do on Shabbos.
The Gemara implies that according to both Beis Shamai and Beis Hillel, one is forbidden to give ownership of an object on Shabbos (such as to give a gift to someone), but one is permitted to withdraw one's ownership from an object on Shabbos (such as to make one's item Hefker, ownerless). Is this the Halachah?
(a) The BEIS YOSEF (OC 527) infers from the words of the MORDECHAI that in practice one is forbidden to make an acquisition (to give ownership or to acquire ownership) on Shabbos. This is part of the decree that forbids business transactions on Shabbos (see Beitzah 37a). The MAGEN AVRAHAM (OC 306:15) cites the Gemara here as a source for the ruling of the Mordechai. He mentions that this is also the opinion of the RITVA (Kesuvos 4a). The Magen Avraham adds that one may make an acquisition on Shabbos when that acquisition is for the sake of Shabbos or for the sake of a Mitzvah.
However, if one is permitted to make an acquisition for the sake of Shabbos, then why does the Gemara say that one is not permitted to give his share in the Chatzer to the other residents? He is doing so only in order to make the Eruv valid, which is for the sake of Shabbos!
The answer is that the Gemara says specifically that "Makneh Reshus" is forbidden. Giving away ownership of a Reshus (land) is more stringent than giving a normal gift, and it is not allowed even for the sake of Shabbos.
The difference between acquisitions of land and of other objects seems to be implicit in the words of TOSFOS (DH u'Mikni). Tosfos discusses the prohibition to give away items on Shabbos -- with regard to giving away land. Earlier, however, Tosfos (66a, DH Yafeh Asitem #2), takes for granted that giving a gift (such as permission to use a Chatzer, but not ownership of a Chatzer) on Shabbos is permitted.
(b) The RITVA (see also RASHASH) points out that while the Gemara implies that one may withdraw his ownership from an item on Shabbos (and make it Hefker), perhaps the Gemara permits it only for the sake of making an Eruv, which involves a Mitzvah (as an Eruv is made for the sake of one's Shabbos needs). Consequently, we cannot prove from here that one may withdraw his ownership from an item on Shabbos when one does so not for the sake of a Mitzvah. (See also Ritva to Shabbos 150a, who seems to prohibit one from making an object Hefker on Shabbos.)
2) RELYING ON A "SHITUF MAVO'OS" IN PLACE OF AN "ERUV CHATZEROS"
OPINIONS: There are three situations in which Chatzeros are "joined." First, an Eruv Chatzeros made among the residents of one Chatzer will permit them to carry in that Chatzer. Second, an Eruv Chatzeros made among two or more Chatzeros that open into each other will permit the residents to carry from one Chatzer to another. Third, a Shituf Mavo'os made among Chatzeros that open into a common Mavoy will permit all of the residents to carry in the Mavoy.
The Gemara cites a Beraisa in which Rebbi Meir and the Chachamim disagree about whether a Shituf Mavo'os alone permits the residents to carry in a Mavoy without an Eruv Chatzeros. That is, if the residents of the different Chatzeros did not make an Eruv among themselves to permit them to carry from one Chatzer to another (the second situation mentioned above), but they made a Shituf Mavo'os (the third situation above) to permit them to carry from each Chatzer into the Mavoy, may they rely on the Shituf Mavo'os to permit them to carry from one Chatzer to the other (RASHI, DH b'Somchin a'Shituf and DH Me'arvin)? (The same question applies when they made an Eruv Chatzeros between the Chatzeros, but they did not make a Shituf Mavo'os. May they rely on the Eruv Chatzeros to carry from the Chatzeros into the Mavoy?)
Rebbi Meir says that a Shituf Mavo'os alone does not permit the residents of the Chatzeros to carry from one Chatzer to another. The Rabanan did not permit them to carry when there is only a Shituf Mavo'os, because they were concerned that people might forget or might not realize that there was a Shituf Mavo'os and they might come to carry from one Chatzer to another without an Eruv, even where there is no Shituf. (See Insights to Eruvin 73:1 for further discussion about this concern.)
RASHI (DH Me'arvin) adds that Rebbi Meir agrees that a Shituf Mavo'os permits the residents to carry from one Chatzer to another when an Eruv was made in each individual Chatzer to permit the residents to carry in their respective Chatzer (the first situation mentioned above). In such a case, there is no fear that people will forget the law of Eruv Chatzeros, because they see an Eruv Chatzeros in operation.
Does the Machlokes between Rebbi Meir and the Chachamim also apply to an Eruv Chatzeros in one Chatzer (the first situation mentioned above)? That is, if nothing but a Shituf Mavo'os was made, may the residents of a single Chatzer carry in their Chatzer? We know that in a case of multiple Chatzeros, Rebbi Meir prohibits the residents to carry from one Chatzer to another, and the Chachamim permit them to carry. What do they maintain with regard to carrying from the house into their own Chatzer when only a Shituf Mavo'os was made? Perhaps a Shituf serves not only to join the Chatzeros together, but also serves to join the houses in one Chatzer together. On the other hand, just as an Eruv in one Chatzer certainly does not permit them to carry into the Mavoy or from one Chatzer to another, perhaps a Shituf cannot permit them to carry in one Chatzer.
(a) RASHI (DH Me'arvin) implies that the dispute between Rebbi Meir and the Chachamim applies in the case of a single Chatzer as well. (As Rashi writes, Rebbi Meir maintains that "we do not rely on the Shituf in place of an Eruv when the residents of the Chatzer did not make an Eruv among themselves"). The Chachamim maintain that a Shituf Mavo'os does work in place of an Eruv Chatzeros in one Chatzer, and it permits the residents of that Chatzer to carry into their Chatzer. This also might be the intention of Rashi earlier (DH b'Somchin) when he says, "... and we rely on the Shituf of the Mavoy in place of the Eruv of the Chatzer" (that is, the Eruv of a single Chatzer; however, it is possible that Rashi merely refers to it as the Eruv "of the Chatzer" to differentiate it from the Shituf of the Mavoy). Rebbi Meir disagrees, just as he disagrees with regard to carrying from one Chatzer to another with only a Shituf Mavo'os. (See also Rashi to 73b, DH Rav Lo Tani, where he implies that one does not need an Eruv in a single Chatzer when there is a Shituf Mavo'os.) This is also the opinion of the BACH (OC 387), TAZ, and BI'UR HA'GRA (ibid.).
(b) The RITVA says that it is logical to assert that Rebbi Meir and the Chachamim agree that a Shituf Mavo'os does not permit the residents to carry from the houses of a Chatzer into the Chatzer, because it serves only to unite Chatzeros, and not houses in one Chatzer. This is also the opinion of the BEIS YOSEF (OC 387; see Shulchan Aruch OC 387:1), who asserts that Rashi means to say this as well. (The PIRYO B'ITO attempts to explain how the words of Rashi here can be consistent with the understanding of the Beis Yosef. The Ritva himself, though, asserts that Rashi does not agree with this opinion.)