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Provability with finitely many variables


Author: J. Donald Monk
Journal: Proc. Amer. Math. Soc. 27 (1971), 353-358
MSC: Primary 02.18
MathSciNet review: 0276063
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Abstract: In first-order logic with equality but with finitely many variables, no finite schema suffices to give a sound and complete axiomatization of the universally valid sentences. The proof uses a rather deep result from algebraic logic.


References [Enhancements On Off] (What's this?)

  • [1] Paul R. Halmos, Algebraic logic, Chelsea Publishing Co., New York, 1962. MR 0131961
  • [2] Leon Henkin, Logical systems containing only a finite number of symbols, Séminaire de Mathématiques Supérieures, No. 21, Les Presses de l’Université de Montréal, Montreal, Que., 1967. MR 0239959
  • [3] Leon Henkin and Alfred Tarski, Cylindric algebras, Proc. Sympos. Pure Math., Vol. II, American Mathematical Society, Providence, R.I., 1961, pp. 83–113. MR 0124250
  • [4] Stanisław Jaśkowski, Sur les variables propositionnelles dépendantes, Studia Soc. Sci. Torunensis. Sect. A. 1 (1948), 17–21 (French, with Polish summary). MR 0025418
  • [5] James S. Johnson, Nonfinitizability of classes of representable polyadic algebras, J. Symbolic Logic 34 (1969), 344–352. MR 0256862
  • [6] Donald Kalish and Richard Montague, On Tarski’s formalization of predicate logic with identity, Arch. Math. Logik Grundlagenforsch 7 (1965), 81–101 (1965). MR 0202576
  • [7] J. Donald Monk, Nonfinitizability of classes of representable cylindric algebras, J. Symbolic Logic 34 (1969), 331–343. MR 0256861
  • [8] August Pieczkowski, Undecidability of the homogeneous formulas of degree 3 of the predicate calculus, Studia Logica 22 (1968), 7–16 (English, with Polish and Russian summaries). MR 0236013
  • [9] Alfred Tarski, Contributions to the theory of models. III, Nederl. Akad. Wetensch. Proc. Ser. A. 58 (1955), 56–64 = Indagationes Math. 17, 56–64 (1955). MR 0066303

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276063-5
Keywords: Provability, first-order logic, polyadic algebras, set polyadic algebras, representable polyadic algebras, logically valid sentences, equations holding in polyadic algebras
Article copyright: © Copyright 1971 American Mathematical Society