Re: "Elementary" elements in ZFC.

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Article #1075

#1075

From: John
Date: Sat, 17 Nov 2001 03:42

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torkel@scheutz.sics.se (Torkel Franz?) wrote in message news:<ul0bsi3cmx9.fsf@scheutz.sics.se>...
> john_correy@excite.ca (John) writes:
> 
> 
> > 1. UNRESTRICTED AXIOM OF EXTENSIONALITY OF Z SET THEORY
> > 
> >    AxAy[Az(z in x <-> z in y) ->  x = y]
> > 
> >    (Two sets are equal if, and only if, they have the same members.)
> 
>   Right, and if you add a predicate "x is a set" to the language of
> set theory, you can make "if x and y are sets" explicit.

torkel@scheutz.sics.se (Torkel Franz?) wrote in message news:<ul0bsi3cmx9.fsf@scheutz.sics.se>...
> john_correy@excite.ca (John) writes:
> 
> 
> > 1. UNRESTRICTED AXIOM OF EXTENSIONALITY OF Z SET THEORY
> > 
> >    AxAy[Az(z in x <-> z in y) ->  x = y]
> > 
> >    (Two sets are equal if, and only if, they have the same members.)
> 
>   Right, and if you add a predicate "x is a set" to the language of
> set theory, you can make "if x and y are sets" explicit.

So, equi-membered things are identical only if they are sets?

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From: john_correy@excite.ca (John)
Newsgroups: sci.logic,sci.math,fa.analytic-philosophy
Subject: Re: "Elementary" elements in ZFC.
Date: 16 Nov 2001 19:42:21 -0800
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