Topic Archive: Split principles
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.