Submission date: 6 February 2024

Abstract:

In an important (yet unpublished) research note, Ben Yaacov describes how to turn a global Keisler measures into a type over a monster model of the randomization. This transfer methods allow one to turn questions involving measures into those involving types (in continuous logic). Assuming that T is NIP, we do the following: We verify some of the main claims from that note. We also present some new proofs via the (almost) standardized Keisler measures calculus. We then show that the Morley product commutes with the transfer map for invariant measures. On the other hand, we observe that the Morley product does not commute with the restriction map from random types to global measures. We characterize when the Morley product commutes with the restriction map for pairs of global finitely satisfiable types in the randomization. We end by making some brief observations about the Ellis semigroup in this context.

Mathematics Subject Classification: 03C45, 03C95

Keywords and phrases:

Full text arXiv 2402.04202: pdf, ps.