Samuel Coskey: The Borel ordering on cardinal characteristics

Boise Set Theory Seminar
Thursday, April 4 from 1:30 to 2:30pm
Room: B-309
Speaker: Samuel Coskey
Title: The Borel ordering on cardinal characteristics

Abstract: Many inequalities between cardinal characteristics of the continuum can be proved in a categorical manner. One simply has to exhibit a certain transformation between the two cardinal invariants called a Tukey map. In several applications, the existence of a Tukey map isn’t enough; one must also know the map can be chosen to be definable. For example, although it is easy to show the pseudo-intersection number $\mathfrak p$ lies below the (un)bounding number $\mathfrak b$, it is not clear if the two cardinals are connected by a definable map. In this talk I’ll introduce the core concept, give some examples, and then consider this slightly more challenging question.