To create a space outside the home, like a courtyard, which can be considered part of ones private space for Shabbat, one needs to set aside a food item, representing a meal, in that space. Normally this is not so difficult. But there are times when designating a set-aside item to identify an owned space can be complicated. Two concepts are discussed.
Bererah or "joint ownership" holds when there are multiple owners of a cask of wine, for example. That ownership alone is needed, rather than designating, is shown. But with bererah there is disagreement. That a cask of wine is sufficient, is agreed by the rabbis. But. . .
They only differ where the householders bought a cask of wine in partnership. R. Eleazar b. Taddai is of the opinion that there is no such rule as bererah while the Rabbis maintain that the rule of bererah holds good.
There is another concept of shittuf or "association." By virtue of this association perhaps no meal need be set aside at all.
R. Joseph explained: R. Eleazar b. Taddai and the Rabbis differ on the question whether it is permissible to rely upon shittuf where an ‘erub is required. The one Master holding that It is not permissible to rely on it while the Masters maintain that it is permissible to rely on it.
This term, shittuf, becomes complicated in post-Talmudic literature as dealing with the question of non-Jews who are monotheists - for example Christians who "associate" the name of Jesus when mentioning G-d. The commentators have generally not considered their vow idolatry. Although this is a concept which has caused some confusion, that is not the discussion in the Talmud.