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Projective model completeness

Published online by Cambridge University Press:  12 March 2014

George S. Sacerdote
George S. Sacerdote*
Affiliation:
Institute for Advanced Study, Princeton, New Jersy 08540
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Extract

The concept of model completeness has been very useful in model theory. In this article we obtain a new model theoretic tool by “reversing the arrows.” Specifically, model completeness deals with the relations between a model of a theory and its extensions; in this paper we shall be concerned with the relation between a model of a theory and its homomorphic pre-images.

This work is based on the intuitive principle that metamathematical theorems about universal sentences of the lower predicate calculus and substructures can be translated in a truth-preserving way to theorems about positive sentences and homomorphic images. From model completeness and the completeness theorems which depend on it, this translation gives new criteria for completeness.

Special thanks are due to Professor A. Robinson whose encouragement and suggestions have contributed much to these results.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 1 , March 1974 , pp. 117 - 123
Copyright
Copyright © Association for Symbolic Logic 1974

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References

REFERENCES

[1]Bell, J. L. and Slomson, A. B., Models and ultraproducts, North-Holland, Amsterdam, 1971.Google Scholar
[2]Keisler, H. J., Some applications of infinitely long formulas, this Journal, vol. 30 (1959), pp. 339–349.Google Scholar
[3]Lyndon, R. C., An interpolation theorem in the predicate calculus, Pacific Journal of Mathematics, vol. 9 (1959), pp. 129–142.CrossRefGoogle Scholar
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[5]Robinson, A., Introduction to model theory and the metamathematics of algebra, North-Holland, Amsterdam, 1965.Google Scholar