On Borel sets belonging to every invariant ccc $\sigma $-ideal on $2^{\mathbb {N}}$

DOI10.1090/S0002-9939-2012-11384-XzbMath1264.03097MaRDI QIDQ4907135

Piotr Zakrzewski

Publication date: 4 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Borel setsPolish spacecontinuum hypothesisCantor group\(\sigma\)-idealsproperty (M)countable chain condition (ccc)

Mathematics Subject Classification ID

Descriptive set theory (03E15) Continuum hypothesis and Martin's axiom (03E50) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Other combinatorial set theory (03E05) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10)

Related Items (3)

On invariant ccc \(\sigma\)-ideals on \(2^{\mathbb N}\) ⋮ Differentiability of continuous functions in terms of Haar-smallness ⋮ Haar-smallest sets

Cites Work

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• Covering a Polish group by translates of a nowhere dense set
• Packing index of subsets in Polish groups
• Can ideals without ccc be interesting?
• Fubini properties of ideals
• A Fubini theorem
• The number of translates of a closed nowhere dense set required to cover a Polish group
• On translations of subsets of the real line
• Covering the real line with translates of a zero-dimensional compact set
• On Sets of Vitali's Type
• Covering locally compact groups by less than 2^ωmany translates of a compact nullset
• Iterated products of ideals of Borel sets
• Norms on Possibilities II: More CCC Ideals on 2 ω
• Ideals without ccc
• Skew Products of Ideals
• Perfect cliques and $G_\delta $ colorings of Polish spaces
• Covering $\mathbb R$ with translates of a compact set
• Less than 2^ωmany translates of a compact nullset may cover the real line
• Infinite dimensional perfect set theorems

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