Chain conditions in maximal models

Paul Larson ¹   ; Stevo Todorčević ²

¹ Department of Mathematics University of Toronto Toronto M5S 1A1, Canada
² C.N.R.S. (7056) Université Paris VII 75251 Paris Cedex 05, France

Fundamenta Mathematicae, Tome 168 (2001) no. 1, pp. 77-104

Résumé

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.

Détail

DOI : 10.4064/fm168-1-3

Mots-clés : present mathbb max varations which create maximal models relative certain counterexamples martins axiom hope separating certain classical statements which fall between suslins hypothesis these models taken which maximize relative existence certain type suslin tree force tree resulting model aronszajn trees special knasters forcing axiom cal fails particular interest still question whether cal holds model