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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Tadeusz Dobrowolski, Witold Marciszewski (1995)
Fundamenta Mathematicae
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L. Lewis Jr. (1995)
Fundamenta Mathematicae
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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.
Stanisław Świerczkowski (1995)
Fundamenta Mathematicae
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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 and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.
R. C. Vaughan, T. D. Wooley (1997)
Acta Arithmetica
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E. Bombieri, S. Sperber (1995)
Acta Arithmetica
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Sy Friedman (1997)
Fundamenta Mathematicae
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We present a reformulation of the fine structure theory from Jensen [72] based on his Σ* theory for K and introduce the Fine Structure Principle, which captures its essential content. We use this theory to prove the Square and Fine Scale Principles, and to construct Morasses.