ideals on natural numbers; ultrafilter topology
This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.
 Bartoszyński T., Judah H.: Set Theory. On the Structure of the Real Line
. A K Peters, Wellesley, MA, 1995. MR 1350295
 Kechris A.S.: Classical Descriptive Set Theory
. Graduate Texts in Mathematics, 156, Springer, New York, 1995. MR 1321597
| Zbl 0819.04002
 Thümmel E.: Ramsey theorems and topological dynamics. PhD. Thesis, Charles University of Prague, 1996.
 Todorčević S.: Introduction to Ramsey Spaces
. Annals of Mathematics Studies, 174, Princeton University Press, Princeton, 2010. MR 2603812