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Uncountable categoricity for gross models

Author(s): Michael C. Laskowski; Anand Pillay
Journal: Proc. Amer. Math. Soc. 132 (2004), 2733-2742.
MSC (2000): Primary 03C45; Secondary 03C50, 03C75
Posted: March 25, 2004
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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 $\kappa$.

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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
Email: pillay@math.uiuc.edu

DOI: 10.1090/S0002-9939-04-07451-9
PII: S 0002-9939(04)07451-9
Received by editor(s): June 9, 2003
Posted: 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 of article: Copyright 2004, American Mathematical Society

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