Yair Hayut: Stationary reflection at successors of singulars

Forcing seminar (Tel Aviv University)
Yair Hayut will speak this Tuesday (8/7/14)
(9:10-11, Schreiber 209) his abstract :
Stationary reflection at successors of singulars
I will show how to get, starting with ω supercompact cardinals, a model in which every stationary set at some specific, predefined, successor of singular reflects. This is a simplification of results of Shelah and Magidor for the 80’s and 90’s. The reflection properties obtained this way are indestructible by closed enough forcing, so we can separate some combinatorical properties this way.  For this end, I define the approachability property and show its relations to preservation of stationary sets under closed forcing notions.
If time permits, I’ll show how to obtain Shelah’s model, in which every stationary set that can reflect reflects in the same way.

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