Type: Article

The P-ideal dichotomy, Martin's axiom and entangled sets.

Guzmán, Osvaldo; Todorcevic, Stevo;

Abstract:

We build a model of the P-ideal ichotomy (PID) and Martin’s axiom for ?1 ( ) in which there is a 2-entangled set of reals. In particular, it follows that the Open Graph Axiom or Baumgartner’s axiom for ?1-dense sets are not consequences of . We review Neeman’s iteration method using two type side conditions and provide an alternative proof for the preservation of properness.