Logic & Set Theory Seminar: Getting n-stationary reflection at a non-weakly compact cardinal
Hazel Brickhill, University of Bristol
Howard House 4th Floor Seminar Room
Abstract: We will use Kunen's forcing to get stationary reflection at a non-weakly compact cardinal ("Saturated Ideals", JSL, 1978) to give n-stationary reflection at a non-weakly compact cardinal. Kunen's forcing starts with κ being Π11-indescribable in the ground model but if we add that L is the ground model and in L we have κ is Π1n-indescribable, the same forcing will in fact give us n-stationary reflection at κ in the extension (where κ is non-weakly compact). As Π1n-indescribability is downward absolute to L, this gives us that if the existence of a Π1n-indescribable is consistent, then so is the existence of an n-stationary reflecting cardinal which is not weakly compact.
Organiser: Andrew Brooke-Taylor