Diagonal conditions in ordered spaces

Harold Bennett; David Lutzer

Displaying similar documents to “Diagonal conditions in ordered spaces”

Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

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An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Dense pairs of o-minimal structures

Lou van den Dries (1998)

Fundamenta Mathematicae

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The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

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I prove that the statement that “every linear order of size $2^{ω}$ can be embedded in $(ω^{ω}, ≪)$ ” is consistent with MA + ¬ wKH.

Classification of function spaces with the pointwise topology determined by a countable dense set

Tadeusz Dobrowolski, Witold Marciszewski (1995)

Fundamenta Mathematicae

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Arithmetic progressions of length three in subsets of a random set

Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)

Acta Arithmetica

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Connectedness of the theory of non-surjective injections

Stanisław Świerczkowski (1995)

Fundamenta Mathematicae

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A construction of low-discrepancy sequences using global function fields

Chaoping Xing, Harald Niederreiter (1995)

Acta Arithmetica

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The Arkhangel’skiĭ–Tall problem: a consistent counterexample

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

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We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in ${[ω]}^{ω}$ , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.

Wildness in the product groups

G. Hjorth (2000)

Fundamenta Mathematicae

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Non-abelian Polish groups arising as countable products of countable groups can be tame in arbitrarily complicated ways. This contrasts with some results of Solecki who revealed a very different picture in the abelian case.