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A model of peano arithmetic with no elementary end extension

Published online by Cambridge University Press:  12 March 2014

George Mills
George Mills*
Affiliation:
University of California, Berkeley, CA 94720
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Abstract

We construct a model of Peano arithmetic in an uncountable language which has no elementary end extension. This answers a question of Gaifman and contrasts with the well-known theorem of MacDowell and Specker which states that every model of Peano arithmetic in a countable language has an elementary end extension. The construction employs forcing in a nonstandard model.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 43 , Issue 3 , September 1978 , pp. 563 - 567
Copyright
Copyright © Association for Symbolic Logic 1978

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References

REFERENCES

[1]Gaifman, Haim, Models and types of Peano's arithmetic, Annals of Mathematical Logic, vol. 9 (1976), pp. 223–306.CrossRefGoogle Scholar
[2]MacDowell, R. and Specker, E., Modelle der Arithmetik, Infinitistic Methods, Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 1959, Pergamon Press, New York, Oxford, 1961, pp. 257–263.Google Scholar