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Transactions of the American Mathematical Society

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A trichotomy of countable, stable, unsuperstable theories


Authors: Michael C. Laskowski and S. Shelah
Journal: Trans. Amer. Math. Soc. 363 (2011), 1619-1629
MSC (2010): Primary 03C45
DOI: https://doi.org/10.1090/S0002-9947-2010-05196-7
Published electronically: September 23, 2010
MathSciNet review: 2737280
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Abstract | References | Similar Articles | Additional Information

Abstract: Every countable, strictly stable theory either has the Dimensional Order Property (DOP), is deep, or admits an ‘abelian group witness to unsuperstability’. To obtain this and other results, we develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.


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Additional Information

Michael C. Laskowski
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742

S. Shelah
Affiliation: Department of Mathematics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel – and – Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
MR Author ID: 160185
ORCID: 0000-0003-0462-3152

Received by editor(s): September 24, 2008
Received by editor(s) in revised form: September 2, 2009
Published electronically: September 23, 2010
Additional Notes: The first author was partially supported by NSF grants DMS-0600217 and DMS-0901336.
The second author’s research was partially supported by NSF grants DMS 9704477, DMS 0072560, DMS 0100794 and DMS 0600940 and Israel Science Foundation Grant no. 242/03. Publication 871.
Article copyright: © Copyright 2010 American Mathematical Society