## Journal of Symbolic Logic

### On the Complexity of Propositional Quantification in Intuitionistic Logic

Philip Kremer

#### Abstract

We define a propositionally quantified intuitionistic logic $\mathbf{H}\pi +$ by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that $\mathbf{H}\pi+$ is recursively isomorphic to full second order classical logic. $\mathbf{H}\pi+$ is the intuitionistic analogue of the modal systems $\mathbf{S}5\pi +, \mathbf{S}4\pi +, \mathbf{S}4.2\pi +, \mathbf{K}4\pi +, \mathbf{T}\pi +, \mathbf{K}\pi +$ and $\mathbf{B}\pi +$, studied by Fine.

#### Article information

Source
J. Symbolic Logic, Volume 62, Issue 2 (1997), 529-544.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745241

Mathematical Reviews number (MathSciNet)
MR1464112

Zentralblatt MATH identifier
0887.03002

JSTOR