Completely Ramsey Sets and the Ellentuck Topology | Department of Mathematics

Completely Ramsey Sets and the Ellentuck Topology

Event Information
Event Location: 
GAB 473
Event Date: 
Wednesday, March 23, 2016 - 3:45pm

Ramsey's theorem states that every finite partition of the n-element subsets of N has an infinite homogeneous subset. One might initially hope that the same would hold for finite partitions of the infinite subsets of N. However, assuming the axiom of choice, this is false. This leads one to define a collection A of infinite subsets of N to be Ramsey iff the partition of the infinite subsets of N into A and its complement has an infinite homogeneous subset. To help us study Ramsey sets, we define the Ellentuck topology on the infinite subsets of N. We will show several facts about this topology, our ultimate goal being to prove that A is completely Ramsey iff A has the property of Baire in the Ellentuck topology.