Article View: sci.logic
Article #310Re: Impredicativity - was: Russell's Paradox
From: Randall Holmes
Date: Fri, 06 Nov 1992 19:21
Date: Fri, 06 Nov 1992 19:21
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In article <TORKEL.92Nov5210509@lludd.sics.se> torkel@sics.se (Torkel Franzen) writes:
>In article <1992Nov5.170354.29866@guinness.idbsu.edu> holmes@garnet.idbsu.edu
> (Randall Holmes) writes:
>
> >Neither A nor B can be shown to represent a unique object in ZFC-.
>
> Of course not! The question I was commenting on was whether it
>is provable in ZF without foundation that if there is a function f
>defined on the natural numbers satisfying f(n)={n,f(n+1)}, then there
>is a set x such that x={1,x}, and my answer was that in all likelihood
>this is not so.
You were right; it is easy to construct an interpretation of ZFC- +
VCP (nothing is an iterated element of itself) + existence of
non-well-founded sets.
--
The opinions expressed | --Sincerely,
above are not the "official" | M. Randall Holmes
opinions of any person | Math. Dept., Boise State Univ.
or institution. | holmes@opal.idbsu.edu
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Newsgroups: sci.logic Path: arc1-ca.pugleaf.net!sparky!uunet!pmafire!mica.inel.gov!guinness!garnet.idbsu.edu!holmes From: holmes@garnet.idbsu.edu (Randall Holmes) Subject: Re: Impredicativity - was: Russell's Paradox Message-ID: <1992Nov6.192118.17092@guinness.idbsu.edu> Sender: usenet@guinness.idbsu.edu (Usenet News mail) Nntp-Posting-Host: garnet Organization: Boise State University References: <TORKEL.92Nov5103134@isis.sics.se> <1992Nov5.170354.29866@guinness.idbsu.edu> <TORKEL.92Nov5210509@lludd.sics.se> Date: Fri, 6 Nov 1992 19:21:18 GMT Lines: 21