# Sakae Fuchino: Downward Lowenheim Skolem Theorems for stationary logics and the Continuum Problem

Tuesday, December 11, 2018 17:15

Room: D1-215

Speaker:
Sakae Fuchino

Title: Downward Lowenheim Skolem Theorems for stationary logics and the Continuum Problem

Abstract. Downward Lowenheim Skolem Theorems of extended logics can be considered as reflection principles. In this talk we consider Downward Lowenheim Skolem Theorems of variations of stationary logic. Some of the strongest forms of reflection principles formulated in this way imply CH while some other imply that the continuum is very large. The results presented in this talk are further development of the results presented in the talk I gave last year in Wroclaw and will be a part of a joint paper with Hiroshi Sakai and Andre Ottenbreit Maschio Rodrigues.

# Serhii Bardyla: A topologization of graph inverse semigroups

Tuesday, November 27, 2018 17:15

Room: D1-215

Speaker:
Serhii Bardyla

Title: A topologization of graph inverse semigroups

Abstract. We characterize graph inverse semigroups which admit only discrete locally compact semigroup topology. It will be proved that if a directed graph $$E$$ is strongly connected and contains a finite amount of vertices then a locally compact semitopological graph inverse semigroup $$G(E)$$ is either compact or discrete. We describe graph inverse semigroups which admit compact semigroup topology and construct a universal object in the class of graph inverse semigroups. Embeddings of graph inverse semigroups into compact-like topological semigroups will be investigated. Also, we discuss some open problems.

# Robert Rałowski: Images of Bernstein sets via continuous functions

Tuesday, November 13, 2018 17:15

Room: D1-215

Speaker:
Robert Rałowski

Title: Images of Bernstein sets via continuous functions

Abstract. We examine images of Bernstein sets via continuous mappings. Among other results we prove that there exists a continuous function $$f:\mathbb{R}\to\mathbb{R}$$ that maps every Bernstein subset of $$\mathbb{R}$$ onto the whole real line. This gives the positive answer to a question of Osipov. This talk is based upon joint paper with Jacek Cichoń and Michał Morayne.

# 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 $$\mathfrak b =\mathfrak c$$.