Tree roots, property damage and the law: an update
نویسندگان
چکیده
منابع مشابه
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The following theorems are shown. (A) If ω2 and ω3 have the tree property and either 2א0 = א2 or Ω is measurable thenΠ2 Determinacy holds. (B) If ωn has the tree property for all n < ω, n ≥ 2, and 2<אω = אω then Projective Determinacy holds.
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An important remark is that in the model for the main theorem אω is not strong limit, in particular 21 = אω+2. In doing so we avoid a difficult question of Woodin’s which asks whether it is consistent to have the failure of both SCH and weak square at אω. The main theorem of this paper should be compared with a theorem in [9] where a similar result is obtained for successive failures of weak sq...
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We construct a model in which there are no @n-Aronszajn trees for any nite n 2, starting from a model with innnitely many supercompact cardinals. We also construct a model in which there is no ++-Aronszajn tree for a strong limit cardinal of coonality !, starting from a model with a supercompact cardinal and a weakly compact cardinal above it.
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ژورنال
عنوان ژورنال: Structural Survey
سال: 2002
ISSN: 0263-080X
DOI: 10.1108/02630800210426222