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arXiv · 1508.02034

Soficity for monoids, semigroups, and general dynamical systems

Jan Cannizzo
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Abstract

We examine several definitions of soficity for monoids obtained by generalizing various definitions of sofic groups. They are not all equivalent and include the definition recently introduced by Ceccherini-Silberstein and Coornaert. One of these definitions readily generalizes to semigroups (albeit in an arguably unsatisfying way), thus addressing a question asked by Kambites. We conclude by proposing a definition of soficity for a general dynamical system consisting of a semigroup acting by measure-preserving transformations on a probability space.

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Jan Cannizzo. 2015-08-09. Soficity for monoids, semigroups, and general dynamical systems. https://arxiv.org/abs/1508.02034

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