Martin's axiom

Summary

Martin's axiom, MA, is about partial orders with the countable chain condition. It says that one filter can meet any fewer than continuum many dense sets of such an order. It is a statement about forcing that can be used without forcing, and the precise definition is given separately. It follows from the continuum hypothesis, but it is also consistent with its failure. In that case it decides many questions that ZFC leaves open, for instance Suslin's problem.