Ample thoughts

Daniel Palacin (1) , Frank Olaf Wagner (1)

1 AGL - Algèbre, géométrie, logique

Non-n-ampleness as defined by Pillay and Evans is preserved under analysability. Generalizing this to a more general notion of Sigma-ampleness, we obtain an immediate proof for all simple theories of CHatzidakis weak Canonical Base Property (CBP) for types of finite SU-rank. This is then applied to the special case of groups.

Keywords: stable; simple; one-based; CM-trivial; $n$-ample; internal; analysable; closure; level; flat; ultraflat; canonical base property

Domains: Logic [math.LO]

Daniel Palacin, Frank Olaf Wagner. Ample thoughts. The Journal of Symbolic Logic, 2013, 78 (2), pp.489-510. ⟨10.2178/jsl.7802080⟩. ⟨hal-00581795v5⟩