Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T21:32:39.180Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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