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On the standard part of nonstandard models of set theory

Published online by Cambridge University Press:  12 March 2014

Menachem Magidor
Affiliation:
Hebrew University, Jerusalem, Israel Bar Ilan University, Ramat Gan, Israel
Saharon Shelah
Affiliation:
Hebrew University, Jerusalem, Israel Bar Ilan University, Ramat Gan, Israel
Jonathan Stavi
Affiliation:
Hebrew University, Jerusalem, Israel Bar Ilan University, Ramat Gan, Israel

Abstract

We characterize the ordinals α of uncountable cofinality such that α is the standard part of a nonstandard model of ZFC (or equivalently KP).

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1983

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References

[1]Boolos, G., On the semantics of the constructible levels, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 16 (1970).CrossRefGoogle Scholar
[2]Friedman, H., Countable models of set theory, Cambridge Summer School in Math Logic Springer, Berlin-New York, 1973, pp. 539573.CrossRefGoogle Scholar
[3]Jensen, R., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.CrossRefGoogle Scholar
[4]Magidor, M., Shelah, S. and Stavi, J., Countably decomposable admissible sets, announced in Abstracts of Papers Presented to the American Mathematical Society, 1980, pp. 392393 (in preparation).Google Scholar
[5]Silver, J. H., Some applications of model theory in set theory. Annals of Mathematical Logic, vol. 3 (1971), pp. 45110.CrossRefGoogle Scholar

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