[FOM] Absolutness of arithmetic

[Robert Lubarsky]

As a simple start, take a model of ZF + Con(ZF), and another of ZF + not
Con(ZF). Con(ZF) is an arithmetic statement, so the natural numbers in those
two models differ.

Bob Lubarsky



-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of
Adam Kolany
Sent: Sunday, December 31, 2006 12:25 PM
To: FOM at cs.nyu.edu
Subject: [FOM] Absolutness of arithmetic

Hi,

given a model M of ZF, one can define w model N_M of peano arithmetics 
in the obvious way.
is it known wheather for different M's the models N_M's are elementarily 
equivalent, or one knows an example of two models of ZF which have 
"different"  N_M's ?

ps. Happy New Year.


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