FOM: a question re. completeness

[Kanovei]

>Date: Tue, 3 Feb 1998 10:54:27 -0500
>From: Detlefsen.1 at nd.edu (michael Detlefsen)

>T is
>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.

Vladimir Kanovei