The Tree Property at ω₂ and Bounded Forcing Axioms

Sy-David Friedman; Víctor Torres-Pérez

Displaying similar documents to “The Tree Property at ω₂ and Bounded Forcing Axioms”

Ramification hypothesis again.

Kurepa, Đuro (1988)

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A tree axiom.

Kurepa, Đuro (1985)

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Rudin's Dowker space in the extension with a Suslin tree

Teruyuki Yorioka (2008)

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We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same...

Reduced powers of $ℵ_{2}$ -trees

Keith Devlin (1983)

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A new construction of a Kurepa tree with no Aronszajn subtree

Keith Devlin (1983)

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Collapsing algebras and Suslin trees

Adam Figura (1981)

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Note on a theorem of J. Baumgartner

Keith Devlin (1972)

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A non-special $ω_{2}$ -tree with special $ω_{1}$ -subtrees

Lajos Soukup (1990)

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Proof of a conjecture of McKay

Krister Segerberg (1974)

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Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal

Saharon Shelah, R. Jin (1992)

Fundamenta Mathematicae

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By an $ω_{1}$ - tree we mean a tree of power $ω_{1}$ and height $ω_{1}$ . Under CH and $2^{ω_{1}} > ω_{2}$ we call an $ω_{1}$ -tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between $ω_{1}$ and $2^{ω_{1}}$ . In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus $2^{ω_{1}} > ω_{2}$ that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus $2^{ω_{1}} = ω_{4}$ that there only exist Kurepa trees with $ω_{3}$ -many branches, which answers...