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On the standard part of nonstandard models of set theory

  • Menachem Magidor (a1) (a2), Saharon Shelah (a1) (a2) and Jonathan Stavi (a1) (a2)


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



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[1]Boolos, G., On the semantics of the constructible levels, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 16 (1970).
[2]Friedman, H., Countable models of set theory, Cambridge Summer School in Math Logic Springer, Berlin-New York, 1973, pp. 539573.
[3]Jensen, R., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229308.
[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).
[5]Silver, J. H., Some applications of model theory in set theory. Annals of Mathematical Logic, vol. 3 (1971), pp. 45110.


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