Chain conditions in maximal models

• Autorzy: Paul Larson , Stevo Todorčević
• Języki publikacji: EN

Abstrakty

EN

We present two $ℙ_{max}$ 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 𝒦₃ fails. Of particular interest is the still open question whether 𝒦₂ holds in this model.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E02: Partition relations
• 03E40: Other aspects of forcing and Boolean-valued models
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 168
• Numer: 1
• Strony: 77-104

Daty

wydano

2001

Twórcy

autor

Paul Larson

• Department of Mathematics, University of Toronto, Toronto M5S 1A1, Canada

autor

Stevo Todorčević

• C.N.R.S. (7056), Université Paris VII, 75251 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/fm168-1-3