>
>
> How far should I expect to get? Is there some ceiling that you're 
> anticipating?
>

Yes. Two ceilings: 1) you need a full set of axioms (predicate calculus and 
a set theory) 
2) If you have a constructive logic, you will have to express ideas like: I 
have a proof 
in this state and in all subsequent states but not in that one? How do you 
do that. 

Girard's original work is here.

http://girard.perso.math.cnrs.fr/linear.pdf

And his archives deserve to be read.

http://girard.perso.math.cnrs.fr/Archives.html

The axioms of his predicate calculus is here p. 11.

http://girard.perso.math.cnrs.fr/Synsem.pdf

Unfortunately it is in the Gentzen's style.

-- 
FL

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