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An undecidable two sorted predicate calculus

Published online by Cambridge University Press:  12 March 2014

A. B. Slomson
A. B. Slomson*
Affiliation:
The University of Leeds
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Extract

Let L be a first order predicate language with two sorts of variables and a single dyadic predicate letter whose first place is to be filled by variables of one sort and whose second place is to be filled by variables of the other sort. In answer to a question of M. H. Löb we show that there is no decision procedure for determining whether or not a sentence of L is universally valid.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 1 , 29 May 1969 , pp. 21 - 23
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Kripke, Saul A., A completeness theorem in modal logic, this Journal, vol. 24 (1959), pp. 1–14.Google Scholar
[2]Kripke, Saul A., The undecidability of monadic modal quantification theory, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 113–116.CrossRefGoogle Scholar
[3]Rogers, Hartley Jr., Certain logical reduction and decision problems, Annals of Mathematics, vol. 64 (1956), pp. 264–284.CrossRefGoogle Scholar