On a Notion of Smallness for Subsets of the Baire Space

DOI10.2307/1998505zbMath0401.03022OpenAlexW4214733789MaRDI QIDQ4184827

Alexander S. Kechris

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/1998505

zbMATH Keywords

Baire spacedescriptive set theorydeterminacytwo-person gamesigma-bounded subsetsuperperfect subsetweakly thin subset

Mathematics Subject Classification ID

Descriptive set theory (03E15) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Determinacy principles (03E60)

Related Items (22)

Dominating projective sets in the Baire space ⋮ Regularity properties for dominating projective sets ⋮ Splitting families and forcing ⋮ \(\Delta^ 1_ 2\)-sets of reals ⋮ Indestructibility of ideals and MAD families ⋮ Strongly dominating sets of reals ⋮ On effective \(\sigma\)-boundedness and \(\sigma\)-compactness in Solovay's model ⋮ Strongly unbounded and strongly dominating sets of reals generalized ⋮ Laver trees in the generalized Baire space ⋮ The open dihypergraph dichotomy and the second level of the Borel hierarchy ⋮ The Hurewicz dichotomy for generalized Baire spaces ⋮ Sacks forcing, Laver forcing, and Martin's axiom ⋮ Exact equiconsistency results for \(\Delta_ 3^ 1\)-sets of reals ⋮ Full-splitting Miller trees and infinitely often equal reals ⋮ On Tree Ideals ⋮ Equivalence of Families of Functions on the Natural Numbers ⋮ On effective σ‐boundedness and σ‐compactness ⋮ Needed reals and recursion in generic reals ⋮ Additivity of the two-dimensional Miller ideal ⋮ Antichains of perfect and splitting trees ⋮ Perfect-set properties in \(L(\mathbb{R})[U\)] ⋮ Regularity properties of definable sets of reals

Cites Work

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• Descriptive set theory
• Some measure theoretic results in effective descriptive set theory
• The Theory of Countable Analytical Sets
• Borel sets and hyperdegrees
• Measure and category in effective descriptive set theory
• On the Lebesgue measurability and the axiom of determinateness
• On the axiom of determinateness
• Uniformization in a playful universe

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