Submission date: 19 April 2023

Abstract:

We study the theory of Banach L^p lattices with a distinguished automorphism, in the framework of continuous logic. Using a functional version of the Rokhlin lemma, we prove that it admits a model companion, which is stable and has quantifier elimination. We show that the types of this theory that are not trivial cannot be isolated. We then use this result to obtain a proof of the absence of comeagre conjugacy classes in Aut^*(μ), the Polish group of non-singular transformations of a standard probability space.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2304.09798: pdf, ps.