# Yuan Yuan Zheng: Selective Ultrafilters on FIN

Place: Fields Institute (Room 210)

Date: March 11 , 2016 (13:30-15:00)

Speaker: Yuan Yuan Zheng

Title: Selective Ultrafilters on FIN

Abstract: We give a definition of selective ultrafilters on the collection FIN of all finite nonempty subsets of the set N of natural numbers. We prove that if side-by-side Sacks forcing is applied, then every selective ultrafilter in the ground model generates a selective ultrafilter in the extension. We also show that selective ultrafilters witness the Parametrized Milliken Theorem.