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Undecidability of a Class of Formulas Containing Just One Single-Place Predicate Variable in Modal Calculus

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Studies in Constructive Mathematics and Mathematical Logic

Part of the book series: Seminars in Mathematics ((SM,volume 4))

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Abstract

Below C, A, and S5* will denote the classical, positive (absolute)†† predicate calculus, respectively without functional symbols, and the quantifier extension of the Lewis modal calculus S5 (see [1], for example).

The main results of this note were presented to the Leningrad Seminar on Mathematical Logic on April 7, 1966.

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Literature Cited

  1. Feys, R., “Modèles à variables de différentes sortes pour les logiques modales. μ ou S5,” Synthese, 12(2–3):182–196 (1960).

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  2. Kripke, S. A., “The undecidability of monadic modal quantification theory,” Z. math. Logik und Gründl. Math., 8(2):113–116 (1962).

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  3. Orevkov, V. P., “Some reduction classes and decidable classes of sequents for constructive predicate calculus,” Doklady Akad. Nauk SSSR, 163(l):30–32 (1965).

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  4. Kleene, S. C., Introduction to Metamathematics, Van Nostrand, Princeton, 1950.

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  5. Kleene, S. C., “Permutability of inferences in Gentzen’s calculi LK and LY,” Mem. Am. Math. Soc., No. 10, pp. 1–26 (1952).

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A. O. Slisenko

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Orevkov, V.P. (1969). Undecidability of a Class of Formulas Containing Just One Single-Place Predicate Variable in Modal Calculus. In: Slisenko, A.O. (eds) Studies in Constructive Mathematics and Mathematical Logic. Seminars in Mathematics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8968-2_16

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  • DOI: https://doi.org/10.1007/978-1-4684-8968-2_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8970-5

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