Re: "Elementary" Elements in ZFC.

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Article #1071

#1071

From: John
Date: Thu, 12 Sep 2002 23:18

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Mike Oliver <oliver@math.ucla.edu> wrote in message
news:<3BF949CB.340F494@math.ucla.edu>

> John wrote:
> 
> >  Likewise, if the axiom of extensionality is restricted to
> > sets, only sets are subject to the axiom of extensionality.
> 
> Well, exactly.
>
> > Have you some reason why "extensionality is restricted to sets" should
> > not be understood in the usual way?

> This *is* the usual way.

> I can't figure out what you're worried about.  Suppose you give
> us an example of two essentially different "axioms of extensionality
> restricted to sets".  

Here's the extensionality principle with which you are familiar.

N4 AxAy[Az(z in x <-> z in y) -> x = y]	Classical Extensionality

And here's the extensionality principle you asked that I give.

C4 AxAy[Az(z in x <-> z in y) -> {Et(x in t & y in t) <-> xIy}] Correy
Extensionality

> I don't think you can; there's no remotely
> plausible way of doing so.  Therefore the phrase is not ambiguous.

Well, what about it?  Do you still hold that the phrase
"extensionality restricted to sets" is unambiguous?

--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: 12 Sep 2002 16:18:58 -0700
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