Osvaldo Guzman Gonzalez: There are no P-points in Silver extensions

Place: Fields Institute (Room 210)

Date: September 29 , 2017 (13:30-15:00)

Speaker: Osvaldo Guzman Gonzalez

Title: There are no P-points in Silver extensions

Abstract: We prove that after adding a Silver real no ultrafilter from the ground
model can be extended to a P-point, and this remains to be the case in any
further extension which has the Sacks property. We use this result to show
that there are no P-points in the Silver model or after adding Silver
reals with the side by side product. In particular, we build models with
no P-points where the continuum can be arbitrarily big. This is joint work
with David Chodounský.

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