Rigid P-spaces

Kenneth Kunen

Displaying similar documents to “Rigid P-spaces”

A Corson compact L-space from a Suslin tree

Peter Nyikos (2015)

Colloquium Mathematicae

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The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.

Note on a theorem of J. Baumgartner

Keith Devlin (1972)

Fundamenta Mathematicae

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On a problem of Sikorski

I. Juhász, William Weiss (1978)

Fundamenta Mathematicae

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Reduced powers of $ℵ_{2}$ -trees

Keith Devlin (1983)

Fundamenta Mathematicae

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A non-metrizable collectionwise Hausdorff tree with no uncountable chains and no Aronszajn subtrees

Akira Iwasa, Peter J. Nyikos (2006)

Commentationes Mathematicae Universitatis Carolinae

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It is independent of the usual (ZFC) axioms of set theory whether every collectionwise Hausdorff tree is either metrizable or has an uncountable chain. We show that even if we add “or has an Aronszajn subtree,” the statement remains ZFC-independent. This is done by constructing a tree as in the title, using the set-theoretic hypothesis $♦^{*}$ , which holds in Gödel’s Constructible Universe.

A new construction of a Kurepa tree with no Aronszajn subtree

Keith Devlin (1983)

Fundamenta Mathematicae

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A tree axiom.

Kurepa, Đuro (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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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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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...