Mutually stationary sequences of sets and the non-saturation of the non-stationary ideal on \(P_x(\lambda)\)

DOI10.1007/BF02401842zbMath1017.03022OpenAlexW1499898026MaRDI QIDQ5953843

Matthew Foreman, Menachem Magidor

Publication date: 16 July 2002

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: http://www.actamathematica.org/fulltext.htm

zbMATH Keywords

mutually stationary setsnon-stationary ideal on \(P_\kappa(\lambda)\)saturated ideal

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Other combinatorial set theory (03E05) Ordered sets and their cofinalities; pcf theory (03E04)

Related Items (32)

Mutual stationarity and singular Jonsson cardinals ⋮ Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities ⋮ Canonical structure in the universe of set theory. I ⋮ Remarks on Gitik's model and symmetric extensions on products of the Lévy collapse ⋮ Lower consistency bounds for mutual stationarity with divergent cofinalities and limited covering ⋮ Non-saturation of the nonstationary ideal on \(P _{\kappa }(\lambda )\) in case \(\kappa \leq \mathrm{cf}(\lambda ) < \lambda \) ⋮ On the universality of the nonstationary ideal ⋮ Global square and mutual stationarity at the \(\aleph_n\) ⋮ Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties ⋮ Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse ⋮ The extent of strength in the club filters ⋮ Splitting \({\mathcal P}_\kappa \lambda\) into maximally many stationary sets ⋮ ON SINGULAR STATIONARITY II (TIGHT STATIONARITY AND EXTENDERS-BASED METHODS) ⋮ The Magidor function and diamond ⋮ FORCING AXIOMS, APPROACHABILITY, AND STATIONARY SET REFLECTION ⋮ Nonregular ideals ⋮ Canonical fragments of the strong reflection principle ⋮ A new Löwenheim-Skolem theorem ⋮ On a problem of Foreman and Magidor ⋮ Canonical structure in the universe of set theory. II. ⋮ On the relationship between mutual and tight stationarity ⋮ Towers and clubs ⋮ Game ideals ⋮ Organic and tight ⋮ On singular stationarity. I: Mutual stationarity and ideal-based methods ⋮ Non-saturation of the non-stationary ideal on P _κ (λ) with λ of countable cofinality ⋮ Forcing a mutual stationarity property in cofinality 𝜔₁ ⋮ Ideals on \({P_{\kappa}(\lambda)}\) associated with games of uncountable length ⋮ Guessing more sets ⋮ Tight stationarity and tree-like scales ⋮ Some problems in singular cardinals combinatorics ⋮ Some open problems in mutual stationary involving inner model: a commentary

Cites Work

• Unnamed Item
• Shelah's pcf theory and its applications
• Martin's maximum, saturated ideals, and nonregular ultrafilters. I
• Regularity of ultrafilters and the core model
• Proper forcing
• On the size of closed unbounded sets
• Cofinalities of elementary substructures of structures on \(\aleph_ \omega\)
• Large cardinals and definable counterexamples to the continuum hypothesis
• The extent of strength in the club filters
• Representing Sets of Ordinals as Countable Unions of Sets in the Core Model
• Two Consequences of Determinacy Consistent with Choice
• Stationary subsets of [ℵ_ω^<ω_n]
• Less saturated ideals
• A very weak square principle
• Collapsing successors of singulars
• Potent Axioms

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