Journal of Symbolic Logic

On the Complexity of Propositional Quantification in Intuitionistic Logic

Philip Kremer

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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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745241

Mathematical Reviews number (MathSciNet)
MR1464112

Zentralblatt MATH identifier
0887.03002

JSTOR
links.jstor.org

Citation

Kremer, Philip. On the Complexity of Propositional Quantification in Intuitionistic Logic. J. Symbolic Logic 62 (1997), no. 2, 529--544. https://projecteuclid.org/euclid.jsl/1183745241


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