ZFC+~Con(ZFC)

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2 total messages Started by Timothy Y. Chow Sun, 16 Aug 1992 00:07

#198

Author: Timothy Y. Chow
Date: Sun, 16 Aug 1992 00:07

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Assuming ZFC is consistent, there are models of ZFC+~Con(ZFC).  Are such
models interesting?  Have they been studied?  Or to put it another way, are
there any interesting consequences of assuming that ZFC is INconsistent?
-- 
Tim Chow     tycchow@math.mit.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons.                               ---Popular Mechanics, March 1949

Re: ZFC+~Con(ZFC)

#199

Author: Andrew Dabrowski
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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