The Modal Theory Of Pure Identity And Some Related Decision Problems

Mathematical Logic Quarterly 30 (26-29):415-423 (1984)
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Abstract

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

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Harold Hodes
Cornell University

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References found in this work

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.

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