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ON MAXIMAL STABLE QUOTIENTS OF DEFINABLE GROUPS IN NIP THEORIES

  • MIKE HASKEL (a1) and ANAND PILLAY (a2)

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.

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[1]Casanovas, E., Simple Theories and Hyperimaginaries, Lecture Notes in Logic, Cambridge University Press, New York, Association of Symbolic Logic, 2011.
[2]Chatzidakis, Z. and Hrushovski, E., Model theory of difference fields. Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 29973071.
[3]Hart, B., Kim, B., and Pillay, A., Coordinatisation and canonical bases in simple theories, this Journal, vol. 65 (2000), no. 1, pp. 293309.
[4]Hrushovsk, E., Peterzil, Y., and Pillay, A., Groups, measures, and the NIP. American Mathematical Society, vol. 21 (2008), pp. 563596.
[5]Shelah, S., Minimal bounded index subgroup for dependent theories. Proceedings of the American Mathematical Society, vol. 136 (2008), pp. 10871091.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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