Submission date: 1 April 2011; revised version (with additional author D.P.): 11 October 2011.

Abstract:

We show that 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.

Mathematics Subject Classification: 03C45

Keywords and phrases: stable theory; simple theory; one-based; CM-trivial; n-ample; internal; analysable

Full text arXiv 1104.0179: pdf, ps.