Article View: sci.logic
Article #1072Re: "Elementary" Elements in ZFC.
From: Mike Oliver
Date: Thu, 12 Sep 2002 23:39
Date: Thu, 12 Sep 2002 23:39
31 lines
2936 bytes
2936 bytes
John wrote:
> Mike Oliver <oliver@math.ucla.edu> wrote in message
> news:<3BF949CB.340F494@math.ucla.edu>
>> 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?
This discussion is from almost a year ago; I looked back at
it in groups.google.com and can't figure out why I was ever
interested enough to contribute an article to it. I also don't
know whether you're making a distinction between this predicate "I"
and the equals sign. But then it's not like I really care.
I'll admit in principle that it's possible to make a distinction
based on whether what's "restricted to sets" is the x,y,z or
just the x,y.
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 10ecd1,c20d3ba067ee0f12 X-Google-Attributes: gid10ecd1,public X-Google-Thread: 109d8a,7c953b53ce3f1294 X-Google-Attributes: gid109d8a,public X-Google-Thread: 10cc56,dcd1daaaa2bffb86 X-Google-Attributes: gid10cc56,public X-Google-ArrivalTime: 2002-09-12 16:39:19 PST Path: arc1-ca.pugleaf.net!archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.icl.net!newsfeed.fjserv.net!opentransit.net!fu-berlin.de!uni-berlin.de!ts14-51.dialup.bol.ucla.EDU!not-for-mail From: Mike Oliver <oliver@math.ucla.edu> Newsgroups: sci.logic,sci.math,fa.analytic-philosophy Subject: Re: "Elementary" Elements in ZFC. Date: Thu, 12 Sep 2002 16:39:07 -0700 Organization: UCLA Lines: 31 Message-ID: <3D81259B.ED8BF3C7@math.ucla.edu> References: <87ofbg4xg8.fsf@phiwumbda.localnet> <87u1l72uno.fsf@phiwumbda.localnet> <70f94e16.0209032113.457a9346@posting.google.com> <877ki1kcg7.fsf@phiwumbda.localnet> <70f94e16.0209051730.516807fd@posting.google.com> <ms5hnukf7v3iep4lja9ktnv3rab8ojqcql@4ax.com> <70f94e16.0209061301.60ae34e6@posting.google.com> <149inu09dp31ttfg81e0idabl0av7omb3a@4ax.com> <xesbs741m0z.fsf@eagle.cs.unc.edu> <i7ivnu8su4cpq4oj0tflsvlr1bh990q43p@4ax.com> <xes65xb5b94.fsf@atlanta.cs.unc.edu> <70f94e16.0209121518.7fc29f0b@posting.google.com> NNTP-Posting-Host: ts14-51.dialup.bol.ucla.edu (164.67.24.60) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: fu-berlin.de 1031873957 486449 164.67.24.60 (16 [136402]) X-Mailer: Mozilla 4.75 [en] (WinNT; U) X-Accept-Language: it,en