Re: "Elementary" elements in ZFC.

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Article #1084

#1084

From: John
Date: Thu, 15 Nov 2001 22:51

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torkel@scheutz.sics.se (Torkel Franz?) wrote in message news:<ul0lmh8ckve.fsf@scheutz.sics.se>...
> john_correy@excite.ca (John) writes:
> 
> > > > Would you mind formulating your principle of restricted extensionality?
> > > 
> > >   If sets X and Y have the same members, X=Y.
> > 
> > Does every mathie hatch like this?
> 
>   Well, is there anything you find obscure about the principle?


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.)

2. RESTRICTED AXIOM OF EXTENSIONALITY OF FRANZEN SET THEORY

         ?                ?                  ?

   (If sets X and Y have the same members, they are equal.)

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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: 15 Nov 2001 14:51:52 -0800
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