Displaying similar documents to “Selections that characterize topological completeness”

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Teresa Bigorajska, Henryk Kotlarski, James Schmerl (1998)

Fundamenta Mathematicae

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We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.

Measures on Corson compact spaces

Kenneth Kunen, Jan van Mill (1995)

Fundamenta Mathematicae

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We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.

Near metric properties of function spaces

P. Gartside, E. Reznichenko (2000)

Fundamenta Mathematicae

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"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.

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.

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*.