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M. Burke (1995)
Review: Moti Gitik, Saharon Shelah, Forcings with ideals and simple forcing notions; M. Gitik, S. Shelah, More on simple forcing Notions and forcing with ideals; D. H. Fremin, Real-valued-measurable cardinalsJournal of Symbolic Logic, 60
R. Rałowski, Szymon Zeberski (2010)
Central European Journal of Mathematics Completely nonmeasurable unions
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E-mail address: szymon.zeberski@pwr.wroc
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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.
Archive for Mathematical Logic – Springer Journals
Published: Dec 7, 2010
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