In 2010, Christoph Weiss isolated a family of strong tree properties that can be used to characterize strongly compact or supercompact cardinals but can also consistently hold at smaller cardinals. For example, the Proper Forcing Axiom implies that even the strongest of these tree properties, ISP, holds at $\omega_2$. In this talk, we will investigate a variety of interactions between these strong tree properties, the existence of (weak) Kurepa trees, and the behavior of the continuum function. Along the way, we will also encounter a variant of Silver's celebrated theorem on cardinal arithmetic dealing with a certain cardinal characteristic of singular cardinals. This is joint work with Sarka Stejskalova.

https://us06web.zoom.us/j/87929792112?pwd=WWNnTkEwOFQwRDdOVXNaK1UzZHBFZz09
Meeting ID: 879 2979 2112
Passcode: 496589