Projective forcing Original Research Article

We study the projective posets and their properties as forcing notions. We also define Martinʹs axiom restricted to projective sets, MA(proj), and show that this axiom is weaker than full Martinʹs axiom by proving the consistency of ZFC + ¬lCH + MA(proj) with “there exists a Suslin tree”, “there exists a non-strong gap”, “there exists an entangled set of reals” and “there exists View the MathML source such that View the MathML source”.