Almost indiscernible sequences and convergence of canonical bases

Details Almost indiscernible sequences and convergence of canonical bases Almost indiscernible sequences and convergence of canonical bases

2009-07-26

arxiv.org/abs/0907.4508v1

Mathematics

Logic

Scientific paper

We study and compare three notions of convergence of types in a stable theory: logic convergence, i.e., formula by formula, metric convergence (both already well studied) and convergence of canonical bases. We characterise sequences which admit almost indiscernible sub-sequences. We study theories for which metric converge coincides with canonical base convergence (\textit{a priori} weaker). For $\aleph_0$-categorical theories we characterise this property by the $\aleph_0$-categoricity of the associated theory of beautiful pairs. In particular, we show that this is the case for the theory of spaces of random variables. Using these tools we give model theoretic proofs for results regarding sequences of random variables appearing in Berkes & Rosenthal \cite{Berkes-Rosenthal:AlmostExchangeableSequences}.

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