Chain conditions in maximal models

Volume 168 / 2001

Paul Larson, Stevo Todorčević Fundamenta Mathematicae 168 (2001), 77-104 MSC: Primary 03E40; Secondary 03E02, 03E35, 03E50. DOI: 10.4064/fm168-1-3


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.


  • Paul LarsonDepartment of Mathematics
    University of Toronto
    Toronto M5S 1A1, Canada
  • Stevo TodorčevićC.N.R.S. (7056)
    Université Paris VII
    75251 Paris Cedex 05, France

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