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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

REFERENCES

[1]Dreben, Burton S. and Goldfarb, Warren D., The decision problem: Solvable classes of quantificational formulas, Addison-Wesley, Reading, Mass., 1979.Google Scholar
[2]Fagin, Ronald, Probabilities on finite models, this Journal, vol. 41 (1976), pp. 5057.Google Scholar
[3]Gödel, Kurt, Zum Entscheidungsproblem des logischen Funktionenkalküls, Monatshefte für Mathematik und Physik, vol. 40 (1933), pp. 433443.CrossRefGoogle Scholar
[4]Goldfarb, Warren D., On the Gödel class with identity, this Journal, vol. 46 (1981), pp. 354364.Google Scholar
[5]Goldfarb, Warren D., Gurevich, Yuri and Shelah, Saharon, On the Gödel class with identity (in preparation).Google Scholar
[6]Kalmar, Laszlo, Über die Erfüllbarkeit derjenigen Zahlausdrucke, welche in der Normalform zwei benachtbarte Allzeichen enthalten, Mathematische Annalen, vol. 108 (1933), pp. 466484.CrossRefGoogle Scholar
[7]Lewis, Harry R., Unsohable classes of quanlificational formulas, Addison-Wesley, Reading, Mass., 1979.Google Scholar
[8]Lewis, Harry R., Complexity results for classes of quantificational formulas, Journal of Computer and System Sciences, vol. 21 (1980), pp. 317353.CrossRefGoogle Scholar
[9]Schütte, Kurt, Untersuchungen zum Entscheidungsproblem der mathematischen Logik, Mathematische Annalen, vol. 109 (1934), pp. 572603.CrossRefGoogle Scholar
[10]Schütte, Kurt, Über die Erfüllbarkeit einer Klasse von logischen Formeln, Mathematische Annalen, vol. 110 (1934), pp. 161194.CrossRefGoogle Scholar