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Seminar on Reckoning

Split Principles and Splitting Families

Kaethe Minden
Marlboro College


Seminar on Reckoning
Wednesday, 23. January 2019 - 11:00 to 15:00

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

The original split principle is an equivalent formulation of a cardinal failing to satisfy the combinatorial essence of weak compactness. The notion was then expanded by Gunter Fuchs and me to characterize the negation of other large cardinal properties. Split principles give rise to seemingly new large cardinals, and some new ideals, for example a normal ideal on Pκλ in the case of λ-Shelahness. In this talk I introduce split principles and connect them to certain new notions of splitting numbers being large.