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Inscribing nonmeasurable sets

Inscribing nonmeasurable sets Our main inspiration is the work in paper (Gitik and Shelah in Isr J Math 124(1):221–242, 2001). We will prove that for a partition $${\mathcal{A}}$$ of the real line into meager sets and for any sequence $${\mathcal{A}_n}$$ of subsets of $${\mathcal{A}}$$ one can find a sequence $${\mathcal{B}_n}$$ such that $${\mathcal{B}_{n}}$$ ’s are pairwise disjoint and have the same “outer measure with respect to the ideal of meager sets”. We get also generalization of this result to a class of σ-ideals posessing Suslin property. However, in that case we use additional set-theoretical assumption about non-existing of quasi-measurable cardinal below continuum. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Inscribing nonmeasurable sets

Archive for Mathematical Logic , Volume 50 (4) – Dec 7, 2010

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer-Verlag
Subject
Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-010-0223-6
Publisher site
See Article on Publisher Site

Abstract

Our main inspiration is the work in paper (Gitik and Shelah in Isr J Math 124(1):221–242, 2001). We will prove that for a partition $${\mathcal{A}}$$ of the real line into meager sets and for any sequence $${\mathcal{A}_n}$$ of subsets of $${\mathcal{A}}$$ one can find a sequence $${\mathcal{B}_n}$$ such that $${\mathcal{B}_{n}}$$ ’s are pairwise disjoint and have the same “outer measure with respect to the ideal of meager sets”. We get also generalization of this result to a class of σ-ideals posessing Suslin property. However, in that case we use additional set-theoretical assumption about non-existing of quasi-measurable cardinal below continuum.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Dec 7, 2010

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