Ample thoughts.(English)Zbl 1311.03063

Summary: Non-$$n$$-ampleness as defined by A. Pillay [ibid. 65, No. 1, 474–480 (2000; Zbl 0945.03047)] and D. M. Evans [ibid. 68, No. 4, 1385–1402 (2003; Zbl 1067.03045)] is preserved under analysability. Generalizing this to a more general notion of $$\Sigma$$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Z. Chatzidakis [“A note on canonical bases and one-based types in supersimple theories”, Confluentes Math. 4, No. 3, Article ID 120004, 34 p. (2012; doi:10.1142/S1793744212500041)] for types of finite SU-rank. This is then applied to the special case of groups.

MSC:

 03C45 Classification theory, stability, and related concepts in model theory 20A15 Applications of logic to group theory

Citations:

Zbl 0945.03047; Zbl 1067.03045
Full Text:

References:

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