A class of consistent anti-Martin’s axioms
John W.L. Merrill · Pacific Journal of Mathematics · 1990
Both the Continuum Hypothesis and Martin's Axiom allow inductive constructions to continue in circumstances where the inductive hypothesis might otherwise fail.The search for useful related axioms procedes naturally in two directions: towards "Super Martin's Axioms," which extend MA to broader classes of orders; and towards "Anti-Martin's Axioms" (AMA's) which are strictly weaker than CH, but which, when combined with ->CH, deny MA.In this paper, we consider restrictions of van Douwen and Fleissner's Undefinable Forcing Axiom which are consistent with the negation of the continuum hypothesis.