Unlimited accumulation by the Shelah's PCF operator

TL;DR

This paper demonstrates, under certain large cardinal assumptions, the existence of a model where the pcf sequence over a set of regular cardinals can be made strictly increasing, answering a previously open question.

Contribution

It constructs a model of set theory with an unbounded increasing pcf sequence, extending Shelah's PCF theory and addressing an open problem.

Findings

Existence of a model with strictly increasing pcf sequence

Under large cardinal assumptions, the sequence can be unbounded

Answers a question from prior research

Abstract

Modulo the existence of large cardinals, there is a model of set theory in which for some set $B$ of regular cardinals, the sequence $\langle \text{pcf}^\alpha(B): \alpha \in \text{Ord} \rangle$ is strictly increasing. The result answers a question from [7].