Submission date: 9 March 2015.

Abstract:

We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures for example in terms of compact systems, entropy and measure algebras. Moreover we study the concept of symbolic representation for models. Amongst the results, we give some characterization of dividing lines and combinatorial configurations such as independence property, order property and strictly order property in terms of symbolic representations.

Mathematics Subject Classification:

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Full text arXiv 1503.02506: pdf, ps.