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Article #297

Re: Foundation, a.k.a. Regularity (was re: Impredicativity - was: Russell's Paradox.)

#297
From: Vaughan R. Pratt
Date: Thu, 05 Nov 1992 17:31
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In article <1992Nov5.112036.17130@husc3.harvard.edu> zeleny@husc10.harvard.edu (Michael Zeleny) writes:
>Vaughan, I shall presume to fill in for Randall by pointing out that
>Schoenfield formulates the Regularity Axiom on p. 326 of the Handbook,
>whereas Takeuti & Zaring describe the same axiom on p. 18 of the first
>edition of their book.  While I am happy to see someone else follow my
>preferred practice of reading into a text whatever one wants to find
>therein, I really wish you would check your sources before wasting the
>time of your audience with this pointless prevarication.

Yes, you're absolutely right, I don't know why I thought it wasn't
there.  I retract what I said about Regularity (Foundation) being
omitted, very sorry.  (This is turning out to be an excellent way for
me to get rid of my misconceptions about set theory.  I hope people
don't object to strongly to my occasional slipups of this kind in this
forum.  Short of investing a lot more time checking everything, the
only alternative I see is for me not to post anything about things I'm
not expert in.)

>This informal procedure can be made rigorous as follows.  The form of
>FA that I find most useful for these purposes is the Axiom Schema of
>Restriction,

Oops, that should have been Regularity.  (Bill's calling it AF was
equally confusing for me, making me think of AntiFoundation.)
-- 
Vaughan Pratt				There's no truth in logic, son.
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Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!CSD-NewsHost.Stanford.EDU!Sunburn.Stanford.EDU!pratt
References: <1992Nov4.161936.12444@guinness.idbsu.edu> <1992Nov4.221041.4812@CSD-NewsHost.Stanford.EDU> <1992Nov5.112036.17130@husc3.harvard.edu>

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Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!CSD-NewsHost.Stanford.EDU!Sunburn.Stanford.EDU!pratt
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Foundation, a.k.a. Regularity (was re: Impredicativity - was: Russell's Paradox.)
Message-ID: <1992Nov5.173131.22564@CSD-NewsHost.Stanford.EDU>
Keywords: foundation (regularity) => cumulative hierarchy
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Organization: Computer Science Department,  Stanford University.
References: <1992Nov4.161936.12444@guinness.idbsu.edu> <1992Nov4.221041.4812@CSD-NewsHost.Stanford.EDU> <1992Nov5.112036.17130@husc3.harvard.edu>
Date: Thu, 5 Nov 1992 17:31:31 GMT
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