The seminar meets on Wednesday January 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Miha Habic — The ultrapower capturing property (part I)
In 1993 Cummings showed that it is consistent (relative to large
cardinals) that there is a measurable cardinal kappa carrying a normal
measure whose ultrapower contains the whole powerset of kappa^+. He
showed that nontrivial large cardinal strength was necessary for this,
but it was not clear whether this capturing property had any direct
consequences. Recently Radek Honzík and I showed that it is relatively
consistent that the least measurable cardinal has this capturing
property. We also considered a local version of capturing. In this talk
I will overview the necessary large cardinal machinery and Cummings’
The second part of the talk will take place on Wednesday January 16th.
In the second talk Miha will introduce a forcing notion due to Apter and
Shelah and the modifications necessary to obtain the result.