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A definable nonstandard model of the reals

  • Vladimir Kanovei (a1) (a2) and Saharon Shelah (a2) (a3)


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



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[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.
[2]Kanovei, V. and Reeken, M., Internal approach to external sets and universes, Part 1, Studia Logica, vol. 55 (1995), no. 2, pp. 229257.
[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.
[4]Luxemburg, W. A. J., What is nonstandard analysis?, American Mathematics Monthly, vol. 80 (Supplement) (1973), pp. 3867.
[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.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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