On the spectrum of characters of ultrafilters

TL;DR

This paper demonstrates that for a singular cardinal with countable cofinality, the spectrum of characters of ultrafilters can include any set of regular cardinals within a specific range, showing significant flexibility in their structure.

Contribution

It establishes that the character spectrum of ultrafilters at certain singular cardinals can be arbitrarily prescribed within a range, expanding understanding of ultrafilter structures.

Findings

Character spectrum can include any prescribed set of regular cardinals

Spectrum can be manipulated between the singular cardinal and its power set

Shows flexibility in ultrafilter character spectra at singular cardinals

Abstract

We show that the character spectrum $Sp_\chi(\lambda)$, for a singular cardinal $\lambda$ of countable cofinality, may include any prescribed set of regular cardinals between $\lambda$ and $2^\lambda$.