Reflecting stationary sets and successors of singular cardinals

DOI10.1007/BF01370693zbMath0742.03017OpenAlexW2007936948MaRDI QIDQ1179532

Saharon Shelah

Publication date: 26 June 1992

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01370693

zbMATH Keywords

supercompactnesssupercompact cardinalstationary setsLevy collapsesoracle forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35)

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Compactness versus hugeness at successor cardinals ⋮ On properties of theories which preclude the existence of universal models ⋮ Canonical structure in the universe of set theory. I ⋮ Weak Compactness and No Partial Squares ⋮ The approachability ideal without a maximal set ⋮ Borel reductions and cub games in generalised descriptive set theory ⋮ Bounded stationary reflection. II. ⋮ A weak variation of shelah's I[ω₂] ⋮ Cofinalities of elementary substructures of structures on \(\aleph_ \omega\) ⋮ Saturated filters at successors of singulars, weak reflection and yet another weak club principle ⋮ Another method for constructing models of not approachability and not SCH ⋮ In memoriam: James Earl Baumgartner (1943--2011) ⋮ Separating weak partial square principles ⋮ Weak saturation properties and side conditions ⋮ KNASTER AND FRIENDS III: SUBADDITIVE COLORINGS ⋮ Scales with various kinds of good points ⋮ Sigma-Prikry forcing. III: Down to \(\aleph_{\omega}\) ⋮ The canary tree revisited ⋮ Partitioning a reflecting stationary set ⋮ Almost free groups and long Ehrenfeucht-Fraïssé games ⋮ Successive cardinals with no partial square ⋮ Universality: new criterion for non-existence ⋮ Applications of PCF theory ⋮ The generalized continuum hypothesis revisited ⋮ SQUARES, SCALES AND STATIONARY REFLECTION ⋮ THE EIGHTFOLD WAY ⋮ Guessing models and the approachability ideal ⋮ A FORCING NOTION COLLAPSING $\aleph _3 $ AND PRESERVING ALL OTHER CARDINALS ⋮ Mitchell's theorem revisited ⋮ More on simple forcing notions and forcings with ideals ⋮ Non-reflection of the bad set for \(\check{I}_\theta[\lambda\) and pcf] ⋮ Middle diamond ⋮ On SCH and the approachability property ⋮ More on the revised GCH and the black box ⋮ Square and non-reflection in the context of \(\mathcal P_{\kappa}\lambda\) ⋮ Bounded stationary reflection ⋮ 𝐼[𝜔₂ can be the nonstationary ideal on 𝐶𝑜𝑓(𝜔₁)] ⋮ Categoricity of an abstract elementary class in two successive cardinals ⋮ \(\mathrm{ZF}+\mathrm{DC}+\mathrm{AX}_4\) ⋮ Telgársky's conjecture may fail ⋮ Global Chang's conjecture and singular cardinals ⋮ A model of Cummings and Foreman revisited ⋮ Some applications of mixed support iterations ⋮ Shelah's pcf theory and its applications ⋮ The two-cardinals transfer property and resurrection of supercompactness 󠀼span style=󠀢color:red󠀢󠀾This article has been retracted󠀼/span󠀾 ⋮ AN EQUICONSISTENCY RESULT ON PARTIAL SQUARES ⋮ Fake reflection ⋮ On the ideal \(J[\kappa\)] ⋮ Approachability at the second successor of a singular cardinal ⋮ Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals ⋮ HIGHER MILLER FORCING MAY COLLAPSE CARDINALS ⋮ Adding closed unbounded subsets of \(\omega_2\) with finite forcing

Cites Work

• The consistency strength of ``every stationary set reflects
• On power of singular cardinals
• Successors of singulars, cofinalities of reduced products of cardinals and productivity of chain conditions
• On certain indestructibility of strong cardinals and a question of Hajnal
• The primal framework. II: Smoothness
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Jonsson algebras in successor cardinals
• Full reflection of stationary sets below ℵ_ω
• Independence results
• When Does Almost Free Imply Free? (For Groups, Transversals, etc.)

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