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ON MAXIMAL STABLE QUOTIENTS OF DEFINABLE GROUPS IN NIP THEORIES

Published online by Cambridge University Press:  08 February 2018

MIKE HASKEL  and
ANAND PILLAY
MIKE HASKEL
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN46556, USAE-mail:mike.haskel@gmail.com
ANAND PILLAY
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN46556, USA E-mail:apillay@nd.edu
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Abstract

For G a group definable in a saturated model of a NIP theory T, we prove that there is a smallest type-definable subgroup H of G such that the quotient G / H is stable. This generalizes the existence of G00, the smallest type-definable subgroup of G of bounded index.

Keywords

03C4503C60stabilityNIPhyperdefinabilitydefinable groups
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 117 - 122
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

REFERENCES

Casanovas, E., Simple Theories and Hyperimaginaries, Lecture Notes in Logic, Cambridge University Press, New York, Association of Symbolic Logic, 2011.Google Scholar
Chatzidakis, Z. and Hrushovski, E., Model theory of difference fields. Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 2997–3071.Google Scholar
Hart, B., Kim, B., and Pillay, A., Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), no. 1, pp. 293–309.Google Scholar
Hrushovsk, E., Peterzil, Y., and Pillay, A., Groups, measures, and the NIP. American Mathematical Society, vol. 21 (2008), pp. 563–596.Google Scholar
Shelah, S., Minimal bounded index subgroup for dependent theories. Proceedings of the American Mathematical Society, vol. 136 (2008), pp. 1087–1091.Google Scholar