On Variants of CM-triviality

Thomas Blossier (1) , Amador Martin-Pizarro (1) , Frank Olaf Wagner (2)

1 AGL - Algèbre, géométrie, logique
2 ICJ - Institut Camille Jordan

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.

Mots clés: CM-triviality; Canonical Base Property; analysability; internality

Domaines: Logique [math.LO]

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⟩