Chain conditions in maximal models
Tom 168 / 2001
Fundamenta Mathematicae 168 (2001), 77-104
MSC: Primary 03E40; Secondary 03E02, 03E35, 03E50.
DOI: 10.4064/fm168-1-3
Streszczenie
We present two ${\mathbb P}_{\max}$ varations which create maximal models relative to certain counterexamples to Martin's Axiom, in hope of separating certain classical statements which fall between MA and Suslin's Hypothesis. One of these models is taken from $[19]$, in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster's forcing axiom ${\cal K}_{3}$ fails. Of particular interest is the still open question whether ${\cal K}_{2}$ holds in this model.
