Partition properties of ω1 compatible with CH

Abstract

A combinatorial statement concerning ideals of countable subsets of ω1 is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω1,ω*1)-gaps are Hausdorff, and that every coherent sequence on ω1 either almost includes or is orthogonal to some uncountable subset of ω1.