Axiomatic Set Theory -- A question about terminology

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Axiomatic Set Theory -- A question about terminology

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1espresso-hound
Dec 27, 2009, 7:17pm

I own a copy of Patrick Supes' ``Axiomatic Set Theory'', but cannot at the moment find my copy. I need a certain terminology I thought was defined in that text. If someone has the book, please let me know if you can tell me the term I am looking for: Let A and B be sets and let R be a binary relation on their cartesian product, AxB (that is, R is a subset of AxB). Let x be any element of A. Denote by x the set of all y in B for which xRy holds. I think I recall that Suppes calls the set x a ``section'' of the relation R. (Then, if R is an equivalence relation, the sections are called equivalence classes, and they form a partition.) If you have read the book, does this ring a bell?

Also, it is not necessary that I reference Suppes' text, so if any of you have some other text on set theory that discusses the ``sections'' I described above for binary relations, please weigh in and let me know the reference you found.

Thanks in advance, and have a great New Year!

espresso-hound

2espresso-hound
Dec 28, 2009, 8:48am

Ok, I found my copy of Suppes' Axiomatic Set Theory, but the term I was looking for is not ``section''. It is ``coset''. However, I need the corresponding concept for (proper) classes. Please recommend a book that gives a terminology For this concept, if you know of one.

For example, since my classes x are in most cases proper classes, is there a reference that would call them ``coclasses''?