Bulletin of Symbolic Logic 11 (3):428-438 (2005)

Abstract
We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal logics, including those in the standard nomenclature above, even the monadic two-variable fragments turn out to be undecidable
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DOI 10.2178/bsl/1122038996
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References found in this work BETA

A Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
Elements of Intuitionism.Nicolas D. Goodman - 1979 - Journal of Symbolic Logic 44 (2):276-277.
Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1986 - Journal of Symbolic Logic 51 (3):824-824.

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In the Beginning Was Game Semantics?Giorgi Japaridze - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Springer Verlag. pp. 249--350.

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