Re: The Dedekind Snap

Am Tue, 16 Dec 2008 11:25:09 -0800 (PST) schrieb MoeBlee:


One can define 'set' in such theories as Z set theories

What sort of definition did you have in mind?


Note that in this case "0" is a primitive. (Which of course, is not even
that bad an idea, imho. Especially since it allows to introduce the Fregean
i-Operator at a very early stage of the theory. Actually, before stating
any set theoretic axiom.)


c is a class <-> (Ex xec v c=0)

Well, no proper classes in Z (sic!) set theories! ;-)

Hence:

y is a set <-> (Ex xey v y=0)

A very reasonable definition imho: Something is a set if it has some
elements, o r (otherwise) is the empty set (sic!).


u is an urelement <-> ~ u is a set



Herb
.

Relevant Pages

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