Coloring ordinals by reals

Abstract

We introduce several new set-theoretic axioms formulated in terms of coloring of ordinals by reals. We show that these axioms generalize the axioms considered by I.Juhasz, L.Soukup and Z.Szentmiklossy, and give a class of p.o.s including Cohen p.o.-sets which force the axioms. In appearance these axioms are somewhat similar to OCA but it appears that they are inconsistent with OCA.