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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Constructive models of uncountably categorical theories
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by Bernhard Herwig, Steffen Lempp and Martin Ziegler PDF
Proc. Amer. Math. Soc. 127 (1999), 3711-3719 Request permission

Abstract:

We construct a strongly minimal (and thus uncountably categorical) but not totally categorical theory in a finite language of binary predicates whose only constructive (or recursive) model is the prime model.
References
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Additional Information
  • Bernhard Herwig
  • Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England
  • Address at time of publication: Institut für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
  • Email: herwig@amsta.leeds.ac.uk, herwig@ruf.uni-freiburg.de
  • Steffen Lempp
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706-1388
  • MR Author ID: 247988
  • Email: lempp@math.wisc.edu
  • Martin Ziegler
  • Affiliation: Institut für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
  • Email: ziegler@uni-freiburg.de
  • Received by editor(s): October 20, 1997
  • Received by editor(s) in revised form: February 20, 1998
  • Published electronically: May 6, 1999
  • Additional Notes: The first author was supported by a grant of the British Engineering and Physical Sciences Research Council (Research Grant no. GR/K60503)
    The second author’s research was partially supported by NSF grant DMS-9504474 and a grant of the British Engineering and Physical Sciences Research Council (Research Grant no. GR/K60497).
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3711-3719
  • MSC (1991): Primary 03C57, 03D45
  • DOI: https://doi.org/10.1090/S0002-9939-99-04920-5
  • MathSciNet review: 1610909