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Minimal bounded index subgroup for dependent theories
Author(s):
Saharon
Shelah
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1087-1091.
MSC (2000):
Primary 03C45;
Secondary 03C60
Posted:
November 9, 2007
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Abstract:
For a dependent theory  , in  for every type definable group  , the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.
References:
-
- [BaSx76]
- John T. Baldwin and Jan Saxl. Logical stability in group theory. J. Austral. Math. Soc. Ser. A, 21:267-276, 1976. MR 0407151 (53:10934)
- [BOPP05]
- Alessandro Berarducci, Margarita Otero, Yaa'cov Peterzil, and Anand Pillay. A descending chain condition for groups definable in o-minimal structures. Annals of Pure and Applied Logic, 134:303-313, 2005. MR 2139910 (2006a:03052)
- [HPP0x]
- Ehud Hrushovski, Ya'acov Peterzil, and Anand Pillay. Groups, measures, and the NIP. preprint, 2005.
- [Sh:F753]
- Saharon Shelah. Definable Groups for Dependent Theories.
- [Sh:783]
- Saharon Shelah. Dependent first order theories, continued. Israel Journal of Mathematic, accepted. math.LO/0406440.
- [Sh:863]
- Saharon Shelah. Strongly dependent theories. Israel Journal of Mathematics, submitted. math.LO/0504197.
- [Sh:F705]
- Shelah, Saharon. Representation over orders of elementary classes.
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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