Submission date: 13 January 2016.

Abstract:

In [HPP], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that T has the canonical base property in a strong form, internality to being replaced by algebraicity in. In the current paper we give a reasonably robust definition of the strong canonical base property in a rather more general finite rank context than [HPP], and prove its equivalence with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that 1-based groups are rigid.

Mathematics Subject Classification:

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Full text arXiv 1601.03345: pdf, ps.