A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters

Natasha Dobrinen, Stevo Todorcevic

Motivated by Tukey classification problems and building on work in \cite{Dobrinen/Todorcevic11}, we develop a new hierarchy of topological Ramsey spaces ${\mathcal{R}}_{\alpha }$, $\alpha <{\omega }_1$. T…