[FOM] Compactness of second order propositional logic

Dana Scott dana.scott at cs.cmu.edu
Tue Apr 28 14:22:48 EDT 2015

This interesting paper might also be relevant:

Andrew M. Pitts.  On an interpretation of second order quantification 
in first order intuitionistic propositional logic.  The Journal of 
Symbolic Logic, vol. 57 (1992), pp. 33-52.

From the introduction:

This paper establishes a new and rather surprising property
of Heyting’s intuitionistic propositional calculus IpC.  We
show that quantification over propositional variables can be
modelled in IpC, and hence that there is an interpretation
of the second-order propositional calculus IpC2 in IpC which
restricts to the identity on first order propositions. In
order to state this result more precisely, we briefly recall
the syntax and proof theory of first- and second-order
intuitionistic propositional logic.

On Sun, 19 Apr 2015, Guillermo Badia wrote:

> Dear all,
> Are second order propositional languages compact?
> Thanks, Guillermo
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