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.
