Combinatorics of ideals -- selectivity versus density

Prelegent(ci)

Piotr Zakrzewski

Afiliacja

Uniwersytet Warszawski

Termin

10 grudnia 2014 16:15

Pokój

p. 5050

Seminarium

Seminarium „Topologia i teoria mnogości”

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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.

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