Parametrizing by the Ellentuck space

Abstract

We introduce a new construct that can be used to parametrize a topological Ramsey space by the collection of infinite subsets of natural numbers. We show that these parametrized spaces are topological Ramsey spaces. Then we prove a canonical Ramsey theorem for some of the parametrized spaces arising from the construction and conclude with some open questions concerning applications of these canonical Ramsey theorems to the Tukey theory of ultrafilters.