A new class of Ramsey-Classification Theorems and their Applications in the Tukey Theory of Ultrafilters, Parts 1 and 2

@article{Dobrinen2013ANC,
title={A new class of Ramsey-Classification Theorems and their Applications in the Tukey Theory of Ultrafilters, Parts 1 and 2},
author={Natasha Dobrinen and Stevo Todorcevic},
journal={Electronic Notes in Discrete Mathematics},
year={2013},
volume={43},
pages={107-112}
}

Motivated by Tukey classification problems and building on work in Part 1 [5], we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [7], and for each α < ω1, Rα+1 coming immediately after Rα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a rapid p-point satisfying certain partition properties. We prove Ramsey-classification theorems for… CONTINUE READING