David Chodounsky
David Chodounsky: Sacks indestructible ultrafilters and reaping families
19/05/22 14:44
Tuesday, May 24, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: David Chodounsky (Czech Academy of Sciences)
Title: Sacks indestructible ultrafilters and reaping families
Abstract: Preservation of reaping families and especially ultrafilters on countable sets is a well studied theme in set theory of the reals. A. Miller proved that if an ultrafilter remains a reaping family in some forcing extension, then it has to be also Sacks indestructible. The existence of Sacks indestructible ultrafilters in ZFC is an open question. A related problem is Sacks indestructibility of reaping families which are complements of ideals. We prove that complements of most classical ideals are indestructible with one notable exception, the ideal of sets asymptotic density zero.
The presented results are from an upcoming paper with O. Guzman and M. Hrusak.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: David Chodounsky (Czech Academy of Sciences)
Title: Sacks indestructible ultrafilters and reaping families
Abstract: Preservation of reaping families and especially ultrafilters on countable sets is a well studied theme in set theory of the reals. A. Miller proved that if an ultrafilter remains a reaping family in some forcing extension, then it has to be also Sacks indestructible. The existence of Sacks indestructible ultrafilters in ZFC is an open question. A related problem is Sacks indestructibility of reaping families which are complements of ideals. We prove that complements of most classical ideals are indestructible with one notable exception, the ideal of sets asymptotic density zero.
The presented results are from an upcoming paper with O. Guzman and M. Hrusak.
David Chodounsky: Combinatorial properties of the Mathias-Prikry forcing
20/10/16 09:19
Tuesday, October 25, 2016 17:15
Room: D1-215
Speaker: David Chodounsky
Title: Combinatorial properties of the Mathias-Prikry forcing
Abstract. I will review basic fact and results about the Mathias-Prikry forcing and I will present and prove sufficient condition for genericity of reals with respect to this poset. Time permitting, further connections of parameters of the forcing with its properties will be explored.
Room: D1-215
Speaker: David Chodounsky
Title: Combinatorial properties of the Mathias-Prikry forcing
Abstract. I will review basic fact and results about the Mathias-Prikry forcing and I will present and prove sufficient condition for genericity of reals with respect to this poset. Time permitting, further connections of parameters of the forcing with its properties will be explored.