Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Embedding orders into the cardinals with D C κ

Asaf Karagila — 2014

Fundamenta Mathematicae

Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of Z F + D C < κ for any regular κ. We use this theorem to show that for all κ, the assumption of D C κ does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...

Spectra of uniformity

Yair Hayut;  Asaf Karagila — 2019

Commentationes Mathematicae Universitatis Carolinae

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.

Page 1

Download Results (CSV)