Singular cofinality conjecture and a question of Gorelic

TL;DR

This paper proves that, assuming large cardinals, it is consistent to have a proper class of cardinals with cofinality  and their th power exceeding themselves, addressing a question by Gorelic.

Contribution

It demonstrates the consistency, relative to large cardinals, of a class of cardinals with specific cofinality and power properties, answering Gorelic's question.

Findings

Consistency of a proper class of cardinals with cf() and th power properties

Use of large cardinal assumptions to establish the result

Addresses an open question in set theory

Abstract

We give an affirmative answer to a question of Gorelic \cite{Gorelic}, by showing it is consistent, relative to the existence of large cardinals, that there is a proper class of cardinals $\alpha$ with $cf(\alpha)=\omega_1$ and $\alpha^\omega > \alpha.$