1) USING "BEREIRAH" TO MAKE A "SHITUF"
QUESTION: The Gemara teaches that Abaye was unable to make a Shituf in his Mavoy. He could not simply take a barrel of vinegar and be Makneh a Revi'is of vinegar to everyone in the Mavoy and thereby make a valid Shituf, because a Shituf cannot be made with food that is in storage in a barrel. Since the Halachah is that Bereirah does not work ("Ein Bereirah"), it is not possible to determine which specific portion of the vinegar in the barrel belongs to which member of the Mavoy until the members of the Mavoy actually take portions for themselves; their respective portions cannot be determined retroactively.
The Gemara challenges Abaye's reasoning from a Beraisa which states that a Shituf may be made with food in storage. Rav Oshiya answers that the Beraisa follows the opinion of Beis Hillel, who maintains that Bereirah does work, while Abaye's ruling is the opinion of Beis Shamai, who maintains "Ein Bereirah."
Rav Oshiya cites a Mishnah in Ohalos (7:3) as the source for the respective opinions of Beis Shamai and Beis Hillel. The Mishnah discusses a case of a corpse in a house with many doorways. Although the corpse causes all of the vessels in all of the doorways to become Tamei, Beis Hillel says that opening one of the doors removes the Tum'ah retroactively from the other entranceways. Beis Shamai argues and maintains that opening one of the doors does not remove the Tum'ah retroactively from the other entranceways.
We see from the Mishnah in Ohalos that Beis Hillel maintains that Bereirah works. In the case of the Eruv, therefore, presumably he would hold that a Shituf may be made by one person transferring ownership of a Revi'is of vinegar in a barrel to everyone in the Chatzer. Why, then, did Abaye refrain from making the Shituf? Did he rule like Beis Shamai?
ANSWER: TOSFOS (DH Tanya) answers that Abaye understood the Mishnah in Ohalos differently. He learned that the case of the corpse in the house with many entrances is unrelated to Bereirah, and that Bereirah is not the subject of the Machlokes there between Beis Shamai and Beis Hillel. Rather, the argument there involves Tum'ah l'Mafrei'a. Beis Hillel maintains that it is possible to show retroactively which doorway was Tamei to begin with by opening it later, thus being Metaher all of the other doorways retroactively. (See Rashi to Beitzah 10a, and Insights to Beitzah 38:1.) The subject of Bereirah is a Machlokes among other Tana'im, as we find earlier (36b-37a), and Abaye followed those Tana'im who maintain "Ein Bereirah."