DEFINABLY AMENABLE NIP GROUPS

被引：29
作者：
Chernikov, Artem [1 ]
Simon, Pierre [2 ]
机构：
[1] Univ Paris Diderot, IMJ PRG, Paris 7, Equipe Log Math, UFR Math Case 7012, F-75205 Paris 13, France
[2] Univ Claude Bernard Lyon 1, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France
来源：
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 31卷 / 03期
基金：
欧洲研究理事会;
关键词：
MODEL-THEORY; CONJECTURE;
D O I：
10.1090/jams/896
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study definably amenable NIP groups. We develop a theory of generics showing that various definitions considered previously coincide, and we study invariant measures. As applications, we characterize ergodic measures, give a proof of the conjecture of Petrykowski connecting existence of bounded orbits with definable amenability in the NIP case, and prove the Ellis group conjecture of Newelski and Pillay connecting the model-theoretic connected component of an NIP group with the ideal subgroup of its Ellis enveloping semigroup. © 2018 American Mathematical Society.
引用
收藏
页码：609 / 641
页数：33
相关论文
共 42 条
  • [1] The structure of approximate groups
    Breuillard, Emmanuel
    Green, Ben
    Tao, Terence
    [J]. PUBLICATIONS MATHEMATIQUES DE L IHES, 2012, (116): : 115 - 221
  • [2] External definability and groups in NIP theories
    Chernikov, Artem
    Pillay, Anand
    Simon, Pierre
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2014, 90 : 213 - 240
  • [3] Externally definable sets and dependent pairs
    Chernikov, Artem
    Simon, Pierre
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 2013, 194 (01) : 409 - 425
  • [4] FORKING AND DIVIDING IN NTP2 THEORIES
    Chernikov, Artem
    Kaplan, Itay
    [J]. JOURNAL OF SYMBOLIC LOGIC, 2012, 77 (01) : 1 - 20
  • [5] Connected components of definable groups and o-minimality I
    Conversano, Annalisa
    Pillay, Anand
    [J]. ADVANCES IN MATHEMATICS, 2012, 231 (02) : 605 - 623
  • [6] Some model theory of SL(2, R)
    Gismatullin, Jakub
    Penazzi, Davide
    Pillay, Anand
    [J]. FUNDAMENTA MATHEMATICAE, 2015, 229 (02) : 117 - 128
  • [7] The structure of tame minimal dynamical systems
    Glasner, Eli
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 1819 - 1837
  • [8] Enveloping semigroups in topological dynamics
    Glasner, Eli
    [J]. TOPOLOGY AND ITS APPLICATIONS, 2007, 154 (11) : 2344 - 2363
  • [9] Halmos Paul Richard, 1950, MEASURE THEORY, V2
  • [10] The Mordell-Lang conjecture for function fields
    Hrushovski, E
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (03) : 667 - 690
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