Uncountable categoricity for gross models
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- by Michael C. Laskowski and Anand Pillay PDF
- Proc. Amer. Math. Soc. 132 (2004), 2733-2742 Request permission
Abstract:
A model $M$ is said to be gross if all infinite definable sets in $M$ have the same cardinality (as $M$). We prove that if for some uncountable $\kappa$, $T$ has a unique gross model of cardinality $\kappa$, then for any uncountable $\kappa$, $T$ has a unique gross model of cardinality $\kappa$.References
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Additional Information
- Michael C. Laskowski
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Email: mcl@math.umd.edu
- Anand Pillay
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 139610
- Email: pillay@math.uiuc.edu
- Received by editor(s): June 9, 2003
- Published electronically: March 25, 2004
- Additional Notes: The first author was partially supported by NSF grant DMS-0071746
The second author was partially supported by NSF grants DMS-0070179 and DMS 01-00979 and a Humboldt Foundation Research Award - Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2733-2742
- MSC (2000): Primary 03C45; Secondary 03C50, 03C75
- DOI: https://doi.org/10.1090/S0002-9939-04-07451-9
- MathSciNet review: 2054800