# Algebra Seminar talk

2022-03-18

David **Chodounsky***P-ultrafilters on natural numbers*

Abstract:

The notion of a P-ultrafilter was introduced by Walter Rudin in 50's and these
objects turned out to be of importance in areas such as topology, set theory
and combinatorics. A breakthrough result of Saharon Shelah from 1977 states
that the existence of P-ultrafilters is not provable using the axioms of ZFC
alone.

The talk will review basic facts about P-ultrafilters and introduce new results concerning their non-existence in certain models of ZFC. The talk should be accessible to a wider audience, only very minimal background on set theory is assumed.