Ultrafilters on 𝜔-their ideals and their cardinal characteristics

Abstract

For a free ultrafilter U \mathcal {U} on ω \omega we study several cardinal characteristics which describe part of the combinatorial structure of U \,\mathcal {U} . We provide various consistency results; e.g. we show how to force simultaneously many characters and many π \pi –characters. We also investigate two ideals on the Baire space ω ω \omega ^{\omega } naturally related to U \mathcal {U} and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.