[FOM] Meta-Logic

[V.Sazonov@csc.liv.ac.uk]

Quoting "Studtmann, Paul" <pastudtmann at davidson.edu> Fri, 11 Aug 2006:

> I am interested in knowing what the weakest systems are that can prove basic
> meta-logical theorems.  For instance, I would like to know whether Peano
> Arithmetic can prove soundness and completeness for first order predicate
> calculus.  Can anyone either state such results or direct me to the relevant
> literature?

In my paper

On existence of complete predicate calculus in metamathematics without 
exponentiation, MFCS'81, Lecture Notes in Computer Science, 118, 
Springer, New York, 1981, P.483--490.

it is shown that in a quite weak framework that completenss of 
first-order logic is equivalent to that of propositional logic, both 
being open questions in that framework. So, in a definite sense, the 
predicate logic is provably complete in that framework iff P=coNP.

Vladimir Sazonov



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