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The existential fragment of second-order propositional intuitionistic logic is undecidable
Journal of Applied Non-Classical Logics 34 (1):55-74 (2024)
Abstract
The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.My notes
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References found in this work
On 2nd order intuitionistic propositional calculus with full comprehension.Dov M. Gabbay - 1974 - Archive for Mathematical Logic 16 (3-4):177-186.
On second order intuitionistic propositional logic without a universal quantifier.Konrad Zdanowski - 2009 - Journal of Symbolic Logic 74 (1):157-167.
Embedding first order predicate logic in fragments of intuitionistic logic.M. H. Löb - 1976 - Journal of Symbolic Logic 41 (4):705-718.
A simple proof of second-order strong normalization with permutative conversions.Makoto Tatsuta & Grigori Mints - 2005 - Annals of Pure and Applied Logic 136 (1-2):134-155.
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