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Random models and the Gödel case of the decision problem

Published online by Cambridge University Press:  12 March 2014

Yuri Gurevich
Affiliation:
University of Michigan, Ann Arbor, Michigan 48109
Saharon Shelah
Affiliation:
Hebrew University, Jerusalem, Israel

Abstract

In a paper of 1933 Gödel proved that every satisfiable first-order ∀2∃* sentence has a finite model. Actually he constructed a finite model in an ingenious and sophisticated way. In this paper we use a simple and straightforward probabilistic argument to establish existence of a finite model of an arbitrary satisfiable ∀2∃* sentence.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1983

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References

[1]Dreben, Burton S. and Goldfarb, Warren D., The decision problem: Solvable classes of quantificational formulas, Addison-Wesley, Reading, Mass., 1979.Google Scholar
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[4]Goldfarb, Warren D., On the Gödel class with identity, this Journal, vol. 46 (1981), pp. 354364.Google Scholar
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