Resumen de The space of infinite partitions of n as a topological Ramsey space

Julian C. Cano, Carlos Augusto di Prisco

• The Ramsey theory of the space of equivalence relations with infinite quotients defined on the set N of natural numbers is an interesting field of research. We view this space as a topological Ramsey space (E∞, ≤, r) and present a game theoretic characterization of the Ramsey property of subsets of E∞. We define a notion of coideal and consider the Ramsey property of subsets of E∞ localized on a coideal H ⊆ E∞. Conditions a coideal H should satisfy to make the structure (E∞, H, ≤, r) a Ramsey space are presented.

  Forcing notions related to a coideal H and their main properties are analyzed.