Article View: sci.logic
Article #52Re: Impredicativity - was: Russell's Paradox.
From: Joshua D. Guttman
Date: Tue, 03 Nov 1992 16:16
Date: Tue, 03 Nov 1992 16:16
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In article <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes: The iterative hierarchy is consistent with Z but not with ZF. Replacement (F) says in effect that any construction you can iterate yields a set. Hence if the universe is an iterative hierarchy it is a set. Anyone brought up on the iterative hierarchy was told a lie. I would have read replacement as saying that any construction you can iterate *through a set* will yield a set. Since the ordinals do not form a set, iterating through them to produce the universe need not yield a set. Josh
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Newsgroups: sci.logic Path: arc1-ca.pugleaf.net!sparky!uunet!think.com!linus!linus.mitre.org!linus!guttman From: guttman@circe.mitre.org (Joshua D. Guttman) Subject: Re: Impredicativity - was: Russell's Paradox. In-Reply-To: pratt@Sunburn.Stanford.EDU's message of Tue, 3 Nov 1992 04:15:15 GMT Message-ID: <GUTTMAN.92Nov3111604@circe.mitre.org> Sender: news@linus.mitre.org (News Service) Nntp-Posting-Host: circe.mitre.org Organization: The MITRE Corporation, Bedford, MA 01730 References: <Bx2ALr.3Az@cantua.canterbury.ac.nz> <1992Nov2.040843.4524@CSD-NewsHost.Stanford.EDU> <1992Nov2.205433.21208@tamsun.tamu.edu> <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU> Date: Tue, 3 Nov 1992 16:16:04 GMT Lines: 15