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Persistence and Herbrand expansions1

Published online by Cambridge University Press:  12 March 2014

Joseph S. Wholey
Joseph S. Wholey*
Affiliation:
Institute for Defense Analyses
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Extract

Following Robinson [3], we say that a first-order sentence S is persistent with respect to a set of sentences K if, whenever S is true in a model M of K, then S is true in every extension of M that is also a model of K. Robinson proved in [3] that:

(T) In order that the sentence S be persistent with respect to the set K it is necessary and sufficient that there be some existential sentence Y such that the sentence S↔Y is deducible from K.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 4 , December 1963 , pp. 280 - 282
Copyright
Copyright © Association for Symbolic Logic 1964

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Footnotes

1

This note is based on part of Chapter 5 of the author's Harvard University dissertation. The author thanks Professors Michael Rabin and Burton Dreben for help in putting the results in their present form.

References

Referentes

[1]Davis, M. and Putnam, H., A computing procedure for quantification theory, Journal of the Association for Computing Machinery, vol. 7 (1960), pp. 201–215.CrossRefGoogle Scholar
[2]Quine, W. V., Interpretations of sets of conditions, this Journal, vol. 19 (1954), pp. 97–102.Google Scholar
[3]Robinson, A., Note on a problem of L. Henkin, this Journal, vol. 21 (1956), pp. 33–35.Google Scholar
[4]Robinson, A., Complete Theories, Amsterdam (North-Holland), 1956.Google Scholar
[5]Tarski, A. and Vaught, R. L., Arithmetical extensions of relational systems, Composltio Mathematica, vol. 13 (1957), pp. 81–102.Google Scholar