Almost disjoint refinement of families of subsets of 𝑁

Abstract

Without any set-theoretic assumptions, we prove that every uniform ultrafilter on the set <italic>N</italic> of all natural numbers has a Comfort system, that is, an almost disjoint refinement. Moreover, we describe one type of ideal such that the family of all subsets of <italic>N</italic> that are not contained in it has an almost disjoint refinement.