Combinatorics of ideals -- selectivity versus density; the second part.

Speaker(s)

Piotr Zakrzewski

Affiliation

Uniwersytet Warszawski

Date

Jan. 14, 2015, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

---

An ideal I on $\omega$ is called:

 - dense if every infinite subset of $\omega$ contains an infinite subset in I,

 - selective if for every partition (A_n) of $\omega$ such that no finite union of elements of the partition is in the dual filter of I there is a selector not in I.

By a result of Mathias, selectivity and density in the case of analytic ideals exclude each other. The talk, based on a joint work with Adam Kwela, will be devoted to some attempts to measure the "distance'' between these properties in terms of ultrafilter topologies of Louveau and countable diagonalizations of Laflamme.

---