The above-mentioned authors introduced the first version of the Open Coloring Axiom in their 1985 paper, showing it to be consistent with ZFC. Though this axiom implies the failure of the CH, it was not known whether it actually decides the value of the continuum to be ℵ₂. The main obstacle in this regard is the construction of so-called "preassignments of colors" (a technical tool necessary for achieving ccc posets), a construction which can only be done over models satisfying the CH.

Recently, Gilton and Neeman have showed that the ARS Open Coloring Axiom is indeed consistent with a larger continuum. In this talk we will discuss in more detail how to force models satisfying this axiom, as well as the difficulties in pushing the continuum above ℵ₂. in such models. Finally, we will outline the solution from the Gilton-Neeman paper.