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March 2009 On second order intuitionistic propositional logic without a universal quantifier
Konrad Zdanowski
J. Symbolic Logic 74(1): 157-167 (March 2009). DOI: 10.2178/jsl/1231082306

Abstract

We examine second order intuitionistic propositional logic, IPC2. Let ℱ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in ℱ that is, for φ∈ℱ, φ is a classical tautology if and only if ¬¬φ is a tautology of IPC2. We show that for each sentence φ∈ℱ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a corollary we obtain a semantic argument that the quantifier ∀ is not definable in IPC2 from ⊥, ∨, ∧, →, ∃.

Citation

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Konrad Zdanowski. "On second order intuitionistic propositional logic without a universal quantifier." J. Symbolic Logic 74 (1) 157 - 167, March 2009. https://doi.org/10.2178/jsl/1231082306

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1163.03010
MathSciNet: MR2499424
Digital Object Identifier: 10.2178/jsl/1231082306

Subjects:
Primary: 03B20

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 1 • March 2009
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