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A counterexample to a conjecture of Scott and Suppes

Published online by Cambridge University Press:  12 March 2014

W. W. Tait
W. W. Tait*
Affiliation:
Stanford University
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Extract

In [1], it is conjectured that if S is a sentence in the first-order functional calculus with identity, and every subsystem of every finite relational system which satisfies S also satisfies S, then S is finitely equivalent to a universal sentence. (Two sentences are finitely equivalent if and only if they are satisfied by the same finite relational systems.) The following sentence S refutes that conjecture, and moreover S is satisfied by all finite subsystems of all (finite or infinite) relational systems which satisfy it.1S contains as predicate letters only the two-place predicate letters ≦, R (and the identity symbol =).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 1 , March 1959 , pp. 15 - 16
Copyright
Copyright © Association for Symbolic Logic 1959

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References

[1]Scott, D. and Suppes, P., Foundational aspects of theories of measure, this Journal, vol. 23 (1958), pp. 113–128.Google Scholar
[2]Tarski, A., Contributions to the theory of models, II, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, ser. A, vol. 57 (1954), pp. 582–588.Google Scholar