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Axiom systems for first order logic with finitely many variables1

Published online by Cambridge University Press:  12 March 2014

James S. Johnson
James S. Johnson*
Affiliation:
University of Hawaii, Honolulu, Hawaii 96822
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Abstract

J. D. Monk has shown that for first order languages with finitely many variables there is no finite set of schema which axiomatizes the universally valid formulas. There are such finite sets of schema which axiomatize the formulas valid in all structures of some fixed finite size.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 4 , December 1973 , pp. 576 - 578
Copyright
Copyright © Association for Symbolic Logic 1973

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Footnotes

1

Thanks are due the referee for several helpful suggestions.

References

REFERENCES

[1] Daigneault, A., Théorie des modèles en logique mathématique, Séminaire de Mathématiques Supérieures, No. 6, Presses Université Montreal, 1963.Google Scholar
[2] Halmos, P. R., Algebraic logic, Chelsea, New York, 1962.Google Scholar
[3] Jonsson, B., Algebras whose congruence lattices are distributive, Mathematica Scandinavica, vol. 21 (1967), pp. 110–121.Google Scholar
[4] Monk, J. D., Provability with finitely many variables, Proceedings of the American Mathematical Society, vol. 27 (1971), pp. 353–358.Google Scholar
[5] Monk, J. D., Nonfinitizability of classes of representable cylindric algebras, this Journal, vol. 34 (1969), pp. 331–343.Google Scholar
[6] Monk, J. D., On equational clcsses of algebraic versions of logic. I, Mathematica Scandinavica, vol. 27 (1970), pp. 53–71.Google Scholar