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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal bounded index subgroup for dependent theories


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 136 (2008), 1087-1091
MSC (2000): Primary 03C45; Secondary 03C60
Published electronically: November 9, 2007
MathSciNet review: 2361885
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Abstract: For a dependent theory $ T$, in $ {\mathfrak{C}}_{T}$ for every type definable group $ G$, the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.


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Additional Information

Saharon Shelah
Affiliation: The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel
Address at time of publication: Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08654-6
PII: S 0002-9939(07)08654-6
Received by editor(s): January 22, 2006
Received by editor(s) in revised form: July 19, 2006, July 30, 2006, and October 19, 2006
Published electronically: November 9, 2007
Additional Notes: The author would like to thank the Israel Science Foundation for partial support of this research (Grant No. 242/03), Publication 876. I would like to thank Alice Leonhardt for the beautiful typing.
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society