Displaying similar documents to “Large free set”

Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that E x t R ( G , G ) = 0 . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...

L ∞ -Khintchine-Bonami inequality in free probability

Artur Buchholz (1998)

Banach Center Publications

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We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ( f = ∑ | w | = l a w ⊗ λ ( w ) ). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

Linear subspace of Rl without dense totally disconnected subsets

K. Ciesielski (1993)

Fundamenta Mathematicae

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In [1] the author showed that if there is a cardinal κ such that 2 κ = κ + then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such...

Vector sets with no repeated differences

Péter Komjáth (1993)

Colloquium Mathematicae

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We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is “yes” if the set is of size at most ℵ 2 , “not” if the set is allowed to be of size ( 2 2 ℵ 0 ) + . It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.

Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

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Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not...

More topological cardinal inequalities

O. Alas (1993)

Colloquium Mathematicae

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A new topological cardinal invariant is defined; it may be considered as a weaker form of the Lindelöf degree.