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

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