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Article #199Re: ZFC+~Con(ZFC)
From: Andrew Dabrowski
Date: Sun, 16 Aug 1992 01:04
Date: Sun, 16 Aug 1992 01:04
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If a model satisfies ~Con(ZFC) then it must actually contain some object which it thinks is a natural number coding a proof of 1=0, say. This object cannot be a standard natural number, or it would mean ZFC really is inconsistent, so it must be a nonstandard number. Hence such a structure models nonstandard arithmetic. I don't know of any systematic treatment of models obtained this way, though. Andrew Dabrowski Try again. Fail again. Fail better. dabrowsa@ucs.indiana.edu -Worstward Ho Indiana U/Bloomington Samuel Beckett
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arc1-ca.pugleaf.net!sparky!uunet!cs.utexas.edu!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!usenet.ucs.indiana.edu!zuni!dabrowsaReferences:
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Newsgroups: sci.logic Path: arc1-ca.pugleaf.net!sparky!uunet!cs.utexas.edu!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!usenet.ucs.indiana.edu!zuni!dabrowsa From: dabrowsa@zuni.ucs.indiana.edu (Andrew Dabrowski) Subject: Re: ZFC+~Con(ZFC) Message-ID: <Bt1xnE.9Mr@usenet.ucs.indiana.edu> Summary: Nonstandard arithmetic Sender: news@usenet.ucs.indiana.edu (USENET News System) Nntp-Posting-Host: zuni.ucs.indiana.edu Organization: UCS, Indiana University, Bloomington, IN References: <1992Aug16.000726.5227@galois.mit.edu> Date: Sun, 16 Aug 1992 01:04:25 GMT Lines: 10