The pcf theory of non fixed points

TL;DR

This paper investigates the behavior of pseudopower functions at singular cardinals that are not fixed points of the aleph function, providing new insights into their set-theoretic properties.

Contribution

It introduces a novel analysis of pseudopower functions at non-fixed point singular cardinals, expanding understanding beyond fixed point cases.

Findings

Characterization of pseudopower values at non-fixed point singular cardinals

Identification of new set-theoretic properties related to these cardinals

Extension of existing theories to broader classes of singular cardinals

Abstract

We deal with values taken by various pseudopower functions at a singular cardinal that is not a fixed point of the aleph function.