Measure-theoretic Suslin Hypothesis
Many authors considered questions about existence of compact ccc non-separable spaces satisfying some additional properties and these questions often motivated quite important theorems. E.g. saying that there is no compact ccc non-separable ordered spaces is just refomulating Suslin's Hypothesis. We study spaces which are not only ccc but which carry strictly positive measures. In particular, we show that consistently each compact space of countable pi-character and supporting a measure is separable.