[FOM] A proof that ZFC has no any omega-models (Joe Shipman)
jaykovfoukzon at list.ru
Sat Feb 23 11:07:00 EST 2013
Let M_ZFC be the statement "ZFC has an model M" and Th be the theory ZFC+M_ZFC.In order to deduce "Th is inconsistent" from Th one have something more than the Th. Let Th# be an extension of Th such that Th proves: Con(Th)<--->Con(Th#). One can use even an maximal extension Th* of Th. Nevertheless in a case when M=omega-model, in order to deduce "Th is inconsistent" from Th,only most Th it is already enough.
>On Feb 8, 2013, at 20:13:57 Joe Shipman JoeShipman at aol.com wrote:
>I would be very surprised if your result holds up, but not because I think there must be an omega-model of ZFC; rather, I doubt ZFC is powerful enough to show there isn't such a model.
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