Polish G-spaces and continuous logic

TL;DR

This paper extends the model theory of Polish G-spaces within continuous logic, broadening the understanding of logic actions of Polish groups beyond previous limitations.

Contribution

It generalizes Becker's model theory to encompass arbitrary Polish groups acting on G-spaces in continuous logic.

Findings

Extended Becker's model theory to all Polish groups

Analyzed logic actions of Polish groups in continuous logic

Provided new frameworks for understanding Polish G-spaces

Abstract

We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.