[FOM] Meta-Logic

[Roger Bishop Jones]

On Friday 11 August 2006 18:51, Studtmann, Paul wrote:
> 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?

Robinsons "Q", which is weaker than PA, has been used for 
meta-logic.  The following paper by Solomon Feferman would 
probably be of interest to you:

"Arithmetisation of metamathematics in a general setting"
Fundamenta Mathematicae XLIX (1960) 

Roger Jones