DMCA
Determinacy and the tree property (2003)
by
Matthew Foreman
,
Menachem Magidor
,
Ralf-dieter Schindler
BibTeX
@MISC{Foreman03determinacyand,
author = {Matthew Foreman and Menachem Magidor and Ralf-dieter Schindler},
title = {Determinacy and the tree property},
year = {2003}
}
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Abstract
The following theorems are shown. (A) If ω2 and ω3 have the tree property and either 2 ℵ0 = ℵ2 or Ω is measurable then Π 1 2 Determinacy holds. (B) If ωn has the tree property for all n < ω, n ≥ 2, and 2 <ℵω = ℵω then Projective Determinacy holds. 1 Introduction. A cardinal δ is said to have the tree property if there is no Aronszajn δtree, i.e., if every tree of height δ all of whose levels have size < δ has a cofinal branch. Hence König’s Lemma states that ω has the tree property, whereas Aronszajn himself discovered that there is an Aronszajn ω1-tree
