Spencer Unger

U. of Toronto

Stationary reflection at successors of singular cardinals

Logic and Set Theory Seminar

3rd February 2021, 4:00 pm – 5:30 pm
Zoom, Online

We survey some recent progress in understanding stationary reflection at successors of singular cardinals and its influence on cardinal arithmetic:

1) In joint work with Yair Hayut, we reduced the consistency strength of stationary reflection at aleph_{omega+1} to an assumption weaker than kappa is kappa+ supercompact.

2) In joint work with Yair Hayut and Omer Ben-Neria, we prove that from large cardinals it is consistent that there is a singular cardinal nu of uncountable cofinality where the singular cardinal hypothesis fails at nu and every collection of fewer than cf(nu) stationary subsets of nu+ reflects at a common point.

The statement in the second theorem was not previously known to be consistent. These results make use of analysis of Prikry generic objects over iterated ultrapowers.

Comments are closed.