A Note on Singular Cardinals in Set Theory Without Choice

TL;DR

This paper explores the behavior of singular cardinals in set theory without the axiom of choice, demonstrating some positive results that contrast with previously known negative consistency results.

Contribution

It provides new provable positive results about singular cardinals without assuming the axiom of choice, challenging prior negative results.

Findings

Certain positive results about singular cardinals are provable without the axiom of choice.

Contrasts with known negative consistency results by Gitik and others.

Poses open problems for further research.

Abstract

We discuss how singular can cardinals be in absence of the axiom of choice. We show that, contrasting with known negative consistency results (of Gitik and others), certain positive results are provable. Then we pose some problems.