Vol. 1, No. 1, 2022

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CM-trivial structures without the canonical base property

Thomas Blossier and Léo Jimenez

Vol. 1 (2022), No. 1, 31–54
DOI: 10.2140/mt.2022.1.31
Abstract

Based on Hrushovski, Palacín and Pillay’s example (Selecta Mathematica 19:4 (2013), 865–877), we produce a new structure without the canonical base property, which is interpretable in Baudisch’s group. Said structure is, in particular, CM-trivial, and thus at the lowest possible level of the ample hierarchy.

Keywords
canonical base property, CM-triviality, Hrushovski constructions, Lie algebras, Baudisch's group
Mathematical Subject Classification
Primary: 03C45, 03C95
Milestones
Received: 15 September 2021
Revised: 15 February 2022
Accepted: 18 February 2022
Published: 24 June 2022
Authors
Thomas Blossier
Université Lyon 1
Institut Camille Jordan
Villeurbanne
France
Léo Jimenez
Université Lyon 1
Institut Camille Jordan
Villeurbanne
France
The Fields Institute for Research in Mathematical Sciences
Toronto, ON
Canada