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

Saharon Shelah; R. Jin

Displaying similar documents to “Planting Kurepa trees and killing Jech-Кunen trees in a model by using one inaccessible cardinal”

Pressing Down Lemma for $λ$ -trees and its applications

Hui Li, Liang-Xue Peng (2013)

Czechoslovak Mathematical Journal

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For any ordinal $λ$ of uncountable cofinality, a $λ$ -tree is a tree $T$ of height $λ$ such that $| T_{α} | < cf (λ)$ for each $α < λ$ , where $T_{α} = {x \in T : ht (x) = α}$ . In this note we get a Pressing Down Lemma for $λ$ -trees and discuss some of its applications. We show that if $η$ is an uncountable ordinal and $T$ is a Hausdorff tree of height $η$ such that $| T_{α} | \leq ω$ for each $α < η$ , then the tree $T$ is collectionwise Hausdorff if and only if for each antichain $C \subset T$ and for each limit ordinal $α \leq η$ with $cf (α) > ω$ , ${ht (c) : c \in C} \cap α$ is not stationary in $α$ . In the last part of this note, we investigate...

Reduced powers of $ℵ_{2}$ -trees

Keith Devlin (1983)

Fundamenta Mathematicae

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

Lajos Soukup (1990)

Commentationes Mathematicae Universitatis Carolinae

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A new construction of a Kurepa tree with no Aronszajn subtree

Keith Devlin (1983)

Fundamenta Mathematicae

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Note on a theorem of J. Baumgartner

Keith Devlin (1972)

Fundamenta Mathematicae

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Constructing Binary Huffman Tree

Hiroyuki Okazaki, Yuichi Futa, Yasunari Shidama (2013)

Formalized Mathematics

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Huffman coding is one of a most famous entropy encoding methods for lossless data compression [16]. JPEG and ZIP formats employ variants of Huffman encoding as lossless compression algorithms. Huffman coding is a bijective map from source letters into leaves of the Huffman tree constructed by the algorithm. In this article we formalize an algorithm constructing a binary code tree, Huffman tree.

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

Teruyuki Yorioka (2008)

Fundamenta Mathematicae

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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...

The Tree Property at ω₂ and Bounded Forcing Axioms

Sy-David Friedman, Víctor Torres-Pérez (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo...

Ramification hypothesis again.

Kurepa, Đuro (1988)

Publications de l'Institut Mathématique. Nouvelle Série

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A tree axiom.

Kurepa, Đuro (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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