A note on canonical bases and one-based types in supersimple theories

Details A note on canonical bases and one-based types in supersimple theories A note on canonical bases and one-based types in supersimple theories

2011-12-30

arxiv.org/abs/1201.0134v2

Mathematics

Logic

Rewrote completely the introduction. Added a few missing hypotheses (finite rank, condition on intersection of algebraic closu

Scientific paper

This paper studies the CBP, a model-theoretic property first discovered by Pillay and Ziegler. We first show a general decomposition result of types of canonical bases, which one can think of as a sort of primary decomposition. This decomposition is then used to show that existentially closed difference fields of any characteristic have the CBP. We also derive consequences of the CBP, and use these results for applications to differential and difference varieties, and algebraic dynamics.

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