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Topic: Models of ZF
Replies: 8   Last Post: Jul 24, 2014 3:36 PM

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Sandy

Posts: 51
Registered: 7/9/13
Models of ZF
Posted: Jul 23, 2014 11:26 AM
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Let

V(0) = emptyset
V(alpha+1) = powerset V(alpha)
V(lambda) = bigcup_{alpha<lambda} V(alpha) if lambda is a limit
ordinal.

If "in" is real is-an-element-of for what alpha is <V(alpha), in> a
model of ZF?

Suppose that U is any class and R is some binary relation on U such that
<U, R> is a model of ZF. Is there always a model of the kind <V(alpha),
in> that is isomorphic to <U, R>? If there is, is there a "recipe" for
finding alpha from U and R?



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