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Journal Articles Fundamenta Mathematicae Year : 2012

On Variants of CM-triviality

Thomas Blossier
  • Function : Author
  • PersonId : 878166
Amador Martin-Pizarro
  • Function : Author
  • PersonId : 878167
Frank Olaf Wagner

Abstract

We introduce a generalization 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 generalizes 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.

Domains

Logic [math.LO]
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Dates and versions

hal-00702683 , version 1 (31-05-2012)
hal-00702683 , version 2 (16-10-2012)

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Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner. On Variants of CM-triviality. Fundamenta Mathematicae, 2012, 219 (3), pp.253-262. ⟨10.4064/fm219-3-4⟩. ⟨hal-00702683v2⟩
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