Model theory of probability spaces with an automorphism

Details Model theory of probability spaces with an automorphism Model theory of probability spaces with an automorphism

2004-05-18

arxiv.org/abs/math/0405360v1

Mathematics

Logic

31 pages

Scientific paper

The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic structures of this kind are exactly the ones isomorphic to the measure algebra of a standard Lebesgue space equipped with an aperiodic measure-preserving automorphism. The corresponding theory is complete and has quantifier elimination; moreover it is stable with built-in canonical bases. We give an intrinsic characterization of its independence relation.

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