Article View: sci.logic
Article #210Re: Non-standard integers.
From: Robert M. Solovay
Date: Tue, 18 Aug 1992 18:55
Date: Tue, 18 Aug 1992 18:55
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1636 bytes
In article <1992Aug18.133344.385@csc.canterbury.ac.nz> wft@math.canterbury.ac.nz (Bill Taylor) writes: > >Thus, the n-tuple-primes conjectures of Hardy would all be false. The only >problem with this whole operation is showing that there can be a model with >*all* the "rows" having such an `n' in them. Kemeny reluctantly left this >loop-hole unplugged. > >-------------------------------------------------------------------------- > Bill Taylor wft@math.canterbury.ac.nz >-------------------------------------------------------------------------- Kemeny's conjecture is false: If M is a non-standard model of PA, then there is a non-standard integer n such that no integer in the "standard row" of n is divisible by all standard integers. To see this, take n which is odd but is divisible by all standard odd integers. If m differs from n by a standard integer, then there must be a standard odd prime which does not divide the difference. Hence m is not divisible by that prime.
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arc1-ca.pugleaf.net!sparky!uunet!cis.ohio-state.edu!magnus.acs.ohio-state.edu!slc3.ins.cwru.edu!agate!math.berkeley.edu!solovayReferences:
<1992Aug17.141017.373@csc.canterbury.ac.nz> <16npkvINNjlq@agate.berkeley.edu> <1992Aug18.133344.385@csc.canterbury.ac.nz>Show Full Headers
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Path: arc1-ca.pugleaf.net!sparky!uunet!cis.ohio-state.edu!magnus.acs.ohio-state.edu!slc3.ins.cwru.edu!agate!math.berkeley.edu!solovay From: solovay@math.berkeley.edu (Robert M. Solovay) Newsgroups: sci.logic Subject: Re: Non-standard integers. Date: 18 Aug 1992 18:55:19 GMT Organization: U.C. Berkeley Math. Department. Lines: 23 Distribution: world Message-ID: <16rh2nINN6og@agate.berkeley.edu> References: <1992Aug17.141017.373@csc.canterbury.ac.nz> <16npkvINNjlq@agate.berkeley.edu> <1992Aug18.133344.385@csc.canterbury.ac.nz> NNTP-Posting-Host: math.berkeley.edu Summary: Kemeny's conjecture is wrong.