The CUNY Graduate Center
In this talk I will introduce various “Split Principles”, which, if they hold, posit the existence of a sequence which in some sense “splits” any large set into two unbounded pieces. We will see that the failure of a particular split principle to hold tends to characterize some large cardinal property; in particular weak compactness, ineffability, measurability and supercompactness can each be characterized in terms of the failure of a split principle. The initial idea of a split principle came about recently in the joint work of Fuchs, Gitman, and Hamkins. The content of the talk is the result of exploring the idea further with Gunter Fuchs.
Kaethe Minden is currently a graduate student in the Ph.D. program in mathematics at the CUNY Graduate Center, studying set theory under the supervision of Gunter Fuchs.