Miha Habic: The ultrapower capturing property (part I)

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’
original argument.

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.

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.

This site uses Akismet to reduce spam. Learn how your comment data is processed.