### 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.

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