# A note on minimal models for pmp actions

## TL;DR

This paper presents a new streamlined construction of a minimal model-universal flow for countable groups, demonstrating that such flows are not unique, and advancing the understanding of invariant measures in dynamical systems.

## Contribution

It introduces a simplified method for constructing minimal model-universal flows, showing their non-uniqueness and expanding the theoretical framework for measure-preserving group actions.

## Key findings

- A new streamlined construction of minimal model-universal flows.
- Proof that minimal model-universal flows are not unique.
- Enhanced understanding of invariant measures in dynamical systems.

## Abstract

Given a countable group $G$, we say that a metrizable flow $Y$ is model-universal if by considering the various invariant measures on $Y$, we can recover every free measure-preserving $G$-system up to isomorphism. Weiss has constructed a minimal model-universal flow. In this note, we provide a new, streamlined construction, allowing us to show that a minimal model-universal flow is far from unique.