A dichotomy for P-ideals of countable sets

Abstract

A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P(ℕ)/fin but also on some higher order statements like for example the existence of Jensen square sequences.