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Article #297Re: Foundation, a.k.a. Regularity (was re: Impredicativity - was: Russell's Paradox.)
From: Vaughan R. Pratt
Date: Thu, 05 Nov 1992 17:31
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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Newsgroups: sci.logic 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 Sender: news@CSD-NewsHost.Stanford.EDU 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 Lines: 26