<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi mathvariant="sans-serif">MA</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="script">I</mml:mi> </mml:math> ) and a failure of

We present a method which forces the failure of Π 3 1 and Σ 3 1 -separation, while MA ( I ) holds, for I the family of indestructible ccc forcings. This shows that, in contrast to the assumption BPFA and ℵ 1 = ℵ 1 L which implies Π 3 1 -separation, that weaker forcing axioms do not decide separation on the third projective level.