# Tukey maps between partial orders

Student Set Theory and Topology Seminar, Toronto, March 2012

*Abstract*: There are many reasons to study Tukey reductions. For instance, many important cardinal invariants can be realized as the cofinality of a partial order. And here, a Tukey reduction between the partial orders corresponds to an inequality between the cardinal invariants.

In the talk I will explain this in more detail, then I will sketch some work of Slawek and Stevo which gives “automatic definability” of Tukey reductions between certain very special partial orders.

PS: Of course, numerous applications to forcing, C*-algebras, and Dominion will be spread homogeneously throughout the talk.