Combinatorics of ideals -- selectivity versus density
- Speaker(s)
- Piotr Zakrzewski
- Affiliation
- Uniwersytet Warszawski
- Date
- Dec. 10, 2014, 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 dovoted to some attempts to measure the "distance'' between these properties in terms of ultrafilter topologies of Louveau and countable diagonalizations of Laflamme.