A dual open coloring axiom

We discuss a dual of the Open Coloring Axiom ( OCA [ ARS ] ) introduced by Abraham et al. [U. Abraham, M. Rubin, S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of ℵ 1 -dense real order types, Ann. Pure Appl. Logic 29 (2) (1985) 123–206] and show that it follows from a statement about continuous colorings on Polish spaces that is known to be consistent. We mention some consequences of the new axiom and show that OCA [ ARS ] implies that all cardinal invariants in Cichoń’s diagram are at least ℵ 2 .