A+ CATEGORY SCIENTIFIC UNIT

On variants of CM-triviality

Volume 219 / 2012

Thomas Blossier, Amador Martin-Pizarro, Frank O. Wagner Fundamenta Mathematicae 219 (2012), 253-262 MSC: Primary 03C45. DOI: 10.4064/fm219-3-4

Abstract

We introduce a generalisation of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalises one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.

Authors

  • Thomas BlossierUniversité de Lyon, CNRS, Université Lyon 1
    Institut Camille Jordan, UMR 5208
    43 boulevard du 11 novembre 1918
    F-69622 Villeurbanne Cedex, France
    e-mail
  • Amador Martin-PizarroUniversité de Lyon, CNRS
    Université Lyon 1, Institut Camille Jordan, UMR 5208
    43 boulevard du 11 novembre 1918
    F-69622 Villeurbanne Cedex, France
    e-mail
  • Frank O. WagnerUniversité de Lyon, CNRS
    Université Lyon 1, Institut Camille Jordan, UMR 5208
    43 boulevard du 11 novembre 1918
    F-69622 Villeurbanne Cedex, France
    e-mail

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