FOM: a question re. completeness
kanovei at wminf2.math.uni-wuppertal.de
Tue Feb 3 13:10:33 EST 1998
>Date: Tue, 3 Feb 1998 10:54:27 -0500
>From: Detlefsen.1 at nd.edu (michael Detlefsen)
>consistency-complete iff for every sentence s of the language of T that is
>not provable in T, if s were provable in T, T would be inconsistent.
This sounds meaningless. To make it meaningful one has
perhaps to separate metamathematical and formal elements.
I would suggest
T is consistency-complete iff for every sentence s of the
language of T that is not provable in T, the following is
a theorem of T:
if Prov_T(s) then \neg Consis s
However I am not sure whether this is meaningful either.
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