Journal of Symbolic Logic 62 (2):529-544 (1997)

Authors
Philip Kremer
University of Toronto at Scarborough
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.
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DOI http://projecteuclid.org/euclid.jsl/1183745241
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Expressivity of Second Order Propositional Modal Logic.Balder ten Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
Pitts' Quantifiers Are Not Topological Quantification.Tomasz Połacik - 1998 - Notre Dame Journal of Formal Logic 39 (4):531-544.
Propositional Quantification in the Topological Semantics for S.Philip Kremer - 1997 - Notre Dame Journal of Formal Logic 38 (2):295-313.

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