May 2018

# Borisa Kuzeljevic: P-ideal dichotomy and versions of the Suslin Hypothesis

Tuesday, May 29, 2018 17:15

Room: D1-215

Speaker:
Borisa Kuzeljevic

Title: P-ideal dichotomy and versions of the Suslin Hypothesis

Abstract. The talk will be about the relationship of P-ideal dichotomy with the statement that all Aronszajn trees are special. This is joint work with Stevo Todorcevic.

# Andrzej Starosolski: The Rudin-Keisler ordering of P-points under b=c

Tuesday, May 15, 2018 17:15

Room: D1-215

Speaker:
Andrzej Starosolski

Title: The Rudin-Keisler ordering of P-points under b=c

Abstract. M. E. Rudin proved under CH that for each P-point there exists another P-point strictly RK-greater . Assuming $$\mathfrak p = \mathfrak c$$, A. Blass showed the same; moreover, he proved that each RK-increasing $$\omega$$-sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-preordering. He also asked what ordinals can be embedded in the set of P-points.

In my talk the results cited above are proved and the mentioned question is answered under a (weaker) assumption $$\mathfrak b =\mathfrak c$$.