Martin's Axiom and Weak Kurepa Hypothesis

Abstract

I show that it is consistent relative to the consistency of a Mahlo cardinal that Martin's axiom holds at $\ddot{I}{‰}_2$, but the weak Kurepa Hypothesis fails. This answers a question posed by Honzik, Lambie-Hanson and Stejskalová. The consistency result is obtained by constructing a model where the weak Kurepa Hypothesis fails in any c.c.c. forcing extension.

It is withdrawn due to a gap in the proof of the main theorem which was pointed out by John Krueger, to whom the author is grateful