Ultrafilters on omega --- their ideals and their cardinal characteristics

Abstract

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