Displaying similar documents to “Ternary positive quadratic forms that represent all odd positive integers”

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.

The Σ* approach to the fine structure of L

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.

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*.