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 \(\mathfrak b =\mathfrak  c\).

Marek Bienias: About universal structures and Fraisse theorem

Tuesday, April 24, 2018 17:15

Room: D1-215

Speaker:
Marek Bienias

Title: About universal structures and Fraisse theorem

Abstract. For a given structure D of language L we can consider age of D, i.e. the family of all finitely generated L-substructures od D. It turns out that age has property (HP) and (JEP). Fraisse theorem let us revers the procedure: if K is nonempty countable family of finitely generated L-structures having properties (HP), (JEP) and (AP), then there exists exactly one (up to isomorphism) L-structure D (so called Fraisse limit) which is countable ultrahomogenous and has age K.
The aim of the talk is to define basic notions from Fraisse theory, proof the main theorem and show some alternative way of looking at the construction of Fraisse limit.

Piotr Borodulin-Nadzieja: Tunnels through topological spaces

Tuesday, April 17, 2018 17:15

Room: D1-215

Speaker:
Piotr Borodulin-Nadzieja

Title: Tunnels through topological spaces

Abstract. I will show a ZFC example of a compact space (without isolated points) through which one cannot drill a tunnel. I will discuss when and when not \(\omega^*\) has a tunnel.

Grzegorz Plebanek: Strictly positive measures on Boolean algebras

Tuesday, March 27, 2018 17:15

Room: D1-215

Speaker:
Grzegorz Plebanek

Title: Strictly positive measures on Boolean algebras

Abstract. \(SPM\) denotes the class of Boolean algebras possessing strictly positive measure (finitely additive and probabilistic). Together with Menachem Magidor, we consider the following problem: Assume that \(B\) belongs to \(SPM\) for every subalgebra \(B\) of a given algebra \(A\) such that \(|B|\le\mathfrak c\). Does it imply that the algebra \(A\) belongs to \(SPM\)?

It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of \(V=L\).