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A definable nonstandard model of the reals

Published online by Cambridge University Press:  12 March 2014

Vladimir Kanovei
Affiliation:
Institute for Information Transmission Problems (IPPI), Russian Academy of Sciences, Bol. Karetnyj Per. 19, Moscow, 127994, Russia, E-mail: kanovei@mccme.ru Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA, E-mail: shelah@math.huji.ac.il, URL: http://www.math.rutgers.edu/~shelah

Abstract

We prove, in ZFC, the existence of a definable, countably saturated elementary extension of the reals.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2004

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References

[1]Chang, C. C. and Keisler, H. J., Model Theory, 3rd ed., Studies in Logic and Foundations of Mathematics, vol. 73, North Holland, Amsterdam, 1992.Google Scholar
[2]Kanovei, V. and Reeken, M., Internal approach to external sets and universes, Part 1, Studia Logica, vol. 55 (1995), no. 2, pp. 229257.CrossRefGoogle Scholar
[3]Keisler, H. J., The hyperreal line, Real numbers, generalizations of reals, and theories of continua (Erlich, P., editor), Kluwer Academic Publishers, 1994, pp. 207237.CrossRefGoogle Scholar
[4]Luxemburg, W. A. J., What is nonstandard analysis?, American Mathematics Monthly, vol. 80 (Supplement) (1973), pp. 3867.CrossRefGoogle Scholar
[5]Solovay, R. M., A model of set theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, vol. 92 (1970), pp. 156.CrossRefGoogle Scholar
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