Sonia Navarro Flores (Universidad Nacional Autónoma de México)

Ramsey spaces and Borel ideals

It is known that the Ellentuck space, which is forcing equivalent to the Boolean algebra $P(\omega)/\operatorname{Fin}$ forces a selective ultrafilter. The Ellentuck space is the prototypical example of a Ramsey space. The connection between Ramsey spaces, ultrafilters, and ideals has been explored in different ways. Ramsey spaces theory has shown to be crucial to investigate Tukey order, Karetov order, and combinatorial properties. This is why we investigate which ideals are related to a Ramsey space in the same sense that the ideal $\operatorname{Fin}$ is related to the Ellentuck space. In this talk, we present some results obtained.