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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: September 23, 2010
MathSciNet review: 2737280
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05196-7
PII: S 0002-9947(2010)05196-7
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