Sacks indestructible ultrafilters and reaping families

Seminarium: 
Topologia
Osoba referująca: 
David Chodounsky (Czech Academy of Sciences)
Data: 
wtorek, 24. Maj 2022 - 17:00
Sala: 
601
Opis: 
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. About 15 minutes before the seminar we invite you for coffee and a chat.