Original Paper

A definable nonstandard enlargement

  1. Frederik Herzberg

Article first published online: 7 MAR 2008

DOI: 10.1002/malq.200710022

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Volume 54, Issue 2, pages 167–175, April 2008

Additional Information

How to Cite

Herzberg, F. (2008), A definable nonstandard enlargement. Mathematical Logic Quarterly, 54: 167–175. doi: 10.1002/malq.200710022

Author Information

  1. Institut für Mathematische Wirtschaftsforschung, Universität Bielefeld, Postfach 10 01 31, D-33501 Bielefeld

Publication History

  1. Issue published online: 7 MAR 2008
  2. Article first published online: 7 MAR 2008
  3. Manuscript Accepted: 24 JUL 2007
  4. Manuscript Revised: 18 JUL 2007
  5. Manuscript Received: 10 JUL 2007
Corrected by:

Addendum: Addendum to “A definable nonstandard enlargement”

Vol. 54, Issue 6, 666–667, Article first published online: 4 NOV 2008

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Keywords:

  • Nonstandard universe;
  • definability;
  • superstructure;
  • ultrapower;
  • elementary embedding

Abstract

This article establishes the existence of a definable (over ZFC), countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers (i.e. bounded with respect to the superstructure hierarchy). The underlying ultrafilter is the one constructed by Kanovei and Shelah [10]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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