Permutation Models Arising From Topological Ideals

TL;DR

This paper explores permutation models derived from topological ideals, demonstrating how certain topological examples can ensure the permutation model satisfies choice principles like countable or well-ordered choice.

Contribution

It provides new topological examples illustrating how permutation models from dynamical ideals can satisfy specific choice axioms.

Findings

Permutation models can satisfy countable choice.

Topological examples illustrate the connection between ideals and choice.

Permutation models can satisfy well-ordered choice.

Abstract

A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this paper, we provide several examples from topology which illustrate using these connections to argue that the corresponding permutation model satisfies either the axiom of countable choice or well-ordered choice.