On completely nonmeasurable unions | Zendy

Żeberski Szymon | Zendy

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On completely nonmeasurable unions

Author(s) -

Żeberski Szymon

Publication year - 2007

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200610024

Subject(s) - mathematics , uncountable set , borel set , polish space , intersection (aeronautics) , ideal (ethics) , borel hierarchy , family of sets , combinatorics , space (punctuation) , generalization , borel equivalence relation , discrete mathematics , countable set , pure mathematics , set (abstract data type) , borel measure , probability measure , mathematical analysis , philosophy , linguistics , engineering , epistemology , computer science , separable space , programming language , aerospace engineering

Assume that there is no quasi‐measurable cardinal not greater than 2 ω . We show that for a c. c. c. σ ‐ideal with a Borel base of subsets of an uncountable Polish space, if is a point‐finite family of subsets from , then there is a subfamily of whose union is completely nonmeasurable, i.e. its intersection with every non‐small Borel set does not belong to the σ ‐field generated by Borel sets and the ideal . This result is a generalization of the Four Poles Theorem (see [1]) and a result from [3]. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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