Nov 16. 2020

P-ultrafilters in Silver extensions

David Chodounsky (Institute of Mathematics, AVCR) will talk about P-ultrafilters in Silver extensions. Time: 16.11.2020, 16:30 Prague time. Write to Radek Honzik to get the Zoom link.

P-ultrafilters are an important and widely used class of ultrafilters on natural numbers. Their existence is however not provable in ZFC. The first model without P-ultrafilters was constructed by Shelah in 1977.  For a long time the method of Shelah was essentially the only known way to get models without P-ultrafilters and many related questions remained 
opened. Many of these questions were settled in our joint paper with O.  Guzman, we proved that there are in fact no P-ultrafilters in the Silver model (and it realtives). I will give a quick overview of this result.