Friday, October 12, 201212:00 amSet theory seminarGC 6417

Generalized Solovay Measures

Nam Trang

University of California at Berkeley

Nam Trang

We will introduce some background and recent progress made in solving the following open problem:

Determine the exact consistency strength of the theory T = ZF + DC + $omega_1$ is supercompact.

It’s known that the upper-bound consistency strength for T is a class of Woodin limits of Woodin cardinals which is (surprisingly) much weaker than ZFC + a supercompact. We will discuss how one might go about computing lower-bounds for T. If time allows, we’ll briefly talk about the relationship of T with the Chang model (CM) and its generalization (CM^+).

Nam Trang is a Ph.D. graduate student studying set theory at the University of California at Berkeley.