Abstract:We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.
Keywords: uniform ultrafilter; axiom of choice; measurable cardinal; strongly compact cardinal
DOI: DOI 10.14712/1213-7243.2019.008
AMS Subject Classification: 03E25 03E55 03E35