Algebra Seminar talk
P-ultrafilters on natural numbers
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.