Does OCA imply the continuum is $\aleph_2$?
Let OCA denote the assertion that every open graph on a separable metric space either has countable chromatic number or else has an uncountable clique. This principle was formulated in the 1980s by Todorcevic in light of the work of Abraham-Rubin-Shelah in which they analyzed a related principle bearing the same name. In 2001, I showed that the formulations of OCA of Abraham-Rubin-Shelah and of Todorcevic taken together imply that the continuum is $\aleph_2$. The question of whether Todorcevic's formulation of OCA settles the value of the continuum remains an open problem. This talk will discuss some partial results and test questions.