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Nonfinitizability of classes of representable polyadic algebras1

Published online by Cambridge University Press:  12 March 2014

James S. Johnson
James S. Johnson*
Affiliation:
University of Colorado
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Extract

The notion of polyadic algebra was introduced by Halmos to reflect algebraically the predicate logic without equality. Later Halmos enriched the study with the introduction of the notion of equality. These algebras are very closely related to the cylindric algebras of Tarski. The notion of diagonal free cylindric algebra predates that of cylindric algebra and is also due to Tarski. The theory of diagonal free algebras forms an important fragment of the theories of polyadic and cylindric algebras.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 344 - 352
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

Research supported by an NSF predoctoral Traineeship. The results of this paper will also appear in the author's doctoral dissertation at the University of Colorado.

References

[1]Daigneault, A. and Monk, D., Representation theory for polyadic algebras, Fundamenta Mathematicae, vol. 52 (1963), pp. 151–176.CrossRefGoogle Scholar
[2]Halmos, P., Algebraic logic. II, Fundamenta Mathematicae, vol. 43 (1956), pp. 255–325.Google Scholar
[3]Halmos, P., Algebraic logic. IV, Transactions of the American Mathematical Society, vol. 86 (1957), pp. 1–27.Google Scholar
[4]Henkin, L. and Tarski, A., Cylindric algebras, Proceedings of symposia in pure mathematics, vol. 2, Amer. Math. Soc., Providence, R.I., 1961, pp. 83–113.CrossRefGoogle Scholar
[5]Monk, J. D., Model-theoretic methods and results in the theory of cylindric algebras, The theory of models, North-Holland, Amsterdam, 1965, pp. 238–250.Google Scholar
[6]Monk, J. D., Nonfinitizability of classes of representable cylindric algebras, this Journal, vol. 34 (1969), pp. 331–343.Google Scholar