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Seminar on Reckoning

The ultrapower capturing property (part I)

Miha Habič


Seminar on Reckoning
Wednesday, 9. January 2019 - 11:00 to 15:00

Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building

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.