Re: "Elementary" elements in ZFC.

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Article #1082

#1082

From: John
Date: Thu, 22 Nov 2001 17:54

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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.

kramsay@aol.commangled (Keith Ramsay) wrote in message news:<20011117095232.15000.00000541@nso-mr.aol.com>
>>
> One standard way of introducing "atoms" into a set theory is
> by allowing the existence of a bunch of things that have no
> members, and are distinct from each other (only one of which
> is a set: {}).
>

If the predicate "x is a set" is added to the language of set theory
and its domain enriched as per above, how does one guarantee that one,
and only one, non-membered thing is a set? By adding an axiom to that
effect?

John

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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: 22 Nov 2001 09:54:27 -0800
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