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Elementary extensions of countable models of set theory

Published online by Cambridge University Press:  12 March 2014

John E. Hutchinson
John E. Hutchinson*
Affiliation:
Stanford University, Stanford, California 94305 State University of New York at Buffalo, Amherst, New York 14226 Australian National University, Canberra, A.C.T. 2600, Australia
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Abstract

We prove the following extension of a result of Keisler and Morley. Suppose is a countable model of ZFC and c is an uncountable regular cardinal in . Then there exists an elementary extension of which fixes all ordinals below c, enlarges c, and either (i) contains or (ii) does not contain a least new ordinal.

Related results are discussed.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 1 , March 1976 , pp. 139 - 145
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Cohen, P. J., A minimal model for set theory, Bulletin of the American Mathematical Society, vol. 69 (1963), pp. 537–540.Google Scholar
[2] Födor, G., Eine Bemerkung zur Theorie der regresiven Funktionen, Acta Universitatis Szegediensis Acta Scientarium Mathematicarium, vol. 17 (1956), pp. 139–142.Google Scholar
[3] Hutchinson, J. E., Order types of ordinals in models of set theory, this Journal (to appear).Google Scholar
[4] Hutchinson, J. E., Model theory via set theory (to appear).Google Scholar
[5] Keisler, H. J. and Morley, M., Elementary extensions of models of set theory, Israel Journal of Mathematics, vol. 6 (1968), pp. 49–65.CrossRefGoogle Scholar
[6] Morley, M., Partitions and models, Proceedings of the Summer School in Logic, Leeds, 1967, Lecture Notes in Mathematics, vol. 70, Springer-Verlag, Berlin, 1968, pp. 109–158.CrossRefGoogle Scholar