On Tree Ideals

DOI10.2307/2161150zbMath0823.03027arXivmath/9311212OpenAlexW2953381850MaRDI QIDQ4845859

Saharon Shelah, Otmar Spinas, Miroslav Repický, Martin Goldstern

Publication date: 17 September 1995

Full work available at URL: https://arxiv.org/abs/math/9311212

zbMATH Keywords

consistencyMiller forcingLaver forcingtree forcingtree ideals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Continuum hypothesis and Martin's axiom (03E50)

Related Items

Cofinality of the Laver ideal ⋮ No Tukey reduction of Lebesgue null to Silver null sets ⋮ Lebesgue's density theorem and definable selectors for ideals ⋮ Filter-Laver measurability ⋮ Strongly dominating sets of reals ⋮ Strongly unbounded and strongly dominating sets of reals generalized ⋮ Different cofinalities of tree ideals ⋮ Laver trees in the generalized Baire space ⋮ Families of sets with nonmeasurable unions with respect to ideals defined by trees ⋮ A Sacks amoeba preserving distributivity of $\mathcal {P}(\omega )/\mathrm {fin}$ ⋮ Forcing indestructibility of MAD families ⋮ Additivity of the two-dimensional Miller ideal ⋮ NONMEASURABLE SETS AND UNIONS WITH RESPECT TO TREE IDEALS ⋮ Antichains of perfect and splitting trees ⋮ Ultrafilters on 𝜔-their ideals and their cardinal characteristics

Cites Work

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• Sacks forcing, Laver forcing, and Martin's axiom
• On the consistency of Borel's conjecture
• The Cichoń diagram
• The space of ultrafilters on N covered by nowhere dense sets
• On completely Ramsey sets
• Iterated perfect-set forcing
• On a Notion of Smallness for Subsets of the Baire Space
• Towers on Trees
• The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing)