Parametrizing by the Ellentuck space
نویسنده
چکیده
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.
منابع مشابه
Parametrizing the abstract Ellentuck theorem
We give a parametrization with perfect subsets of 2∞ of the abstract Ellentuck theorem (see [1], [16] or [17]). The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known classical results like the parametrized version of the Galvin-Prikry theorem due to Miller and Todorcevic [9], and the parametri...
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