A trichotomy of countable, stable, unsuperstable theories
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- by Michael C. Laskowski and S. Shelah PDF
- Trans. Amer. Math. Soc. 363 (2011), 1619-1629 Request permission
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.References
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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. - © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 1619-1629
- MSC (2010): Primary 03C45
- DOI: https://doi.org/10.1090/S0002-9947-2010-05196-7
- MathSciNet review: 2737280