Predictability, topological entropy and invariant random orders

Abstract

We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. On route, we investigate invariant random orders and formulate a unified Kieffer-Pinsker formula for the Kolmogorov-Sinai entropy of measure preserving actions of amenable groups. We also present a proof due to Weiss for the fact that topologically prime actions of sofic groups have non-positive topological sofic entropy.

Harmonic Models and Bernoullicity

“…Equivalently, P is a subsemigroup of G with 1 / ∈ P (we remark that left-invariant partial orders on groups also appeared in [2] but for different reasons). A subset P of G satisfying the above two axioms is called a positive semigroup.…”