Abstract: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.
Keywords: ideals on natural numbers; ultrafilter topology
DOI: DOI 10.14712/1213-7243.2015.203
AMS Subject Classification: 54H05 03E15 03E05