Place: Fields Institute (Room 210)

Date: September 30th, 2016 (13:30-15:00)

Speaker: Zoltan, Vidnyanszky, York University

Title: Characterization of order types representable by Baire class 1 functions

Abstract: Let $\mathcal{F}$ be a family of real valued functions on a Polish space $X$. A natural partial ordering on $\mathcal{F}$ is the pointwise ordering, $\leq_p$. The description of linearly ordered subsets of $(\mathcal{F},\leq_p)$ reveals a lot of information about the poset itself. It turns out that the first interesting family of functions to consider is the family of Baire class 1 functions, $\mathcal{B}_1(X)$. Answering a question of Laczkovich, we give a complete combinatorial characterization of the linearly ordered subsets of $(\mathcal{B}_1(X),\leq_p)$.