Ideals without ccc and without property $ \boldsymbol( \mathbf{M} \boldsymbol)$
نویسندگان
چکیده
منابع مشابه
Ideals without Ccc and without Property (m)
We prove a strong version of a theorem of Balcerzak-RoslanowskiShelah by showing, in ZFC, that there exists a simply definable Borel σ-ideal for which both the ccc and property (M) fail. The proof involves Polish group actions. Definition. A Borel ideal is an ideal I on a Polish space X with the following property: for all A ∈ I, there exists a Borel subset B of X such that A ⊂ B and B ∈ I. We ...
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Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F ⊆ P (X) of size c, consisting of Borel sets which are not in I . Condition (M) states that there is a Borel function f : X → X with f[{x}] / ∈ ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-00-05373-9