On the estimation of certain exponential sums
E. Bombieri, S. Sperber (1995)
Acta Arithmetica
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E. Bombieri, S. Sperber (1995)
Acta Arithmetica
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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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Tadeusz Dobrowolski, Witold Marciszewski (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*.
Rüdiger Göbel, R. Shortt (1994)
Fundamenta Mathematicae
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Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.
Yoshiharu Kohayakawa, Tomasz Łuczak, Vojtěch Rödl (1996)
Acta Arithmetica
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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.