Fragility and indestructibility. II

DOI10.1016/J.APAL.2015.06.002zbMath1373.03101OpenAlexW780820774MaRDI QIDQ490864

Spencer Unger

Publication date: 21 August 2015

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2015.06.002

zbMATH Keywords

fragilityforcinglarge cardinalsindestructibilitytree property

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Other classical set theory (including functions, relations, and set algebra) (03E20)

Related Items (10)

THE TREE PROPERTY AT AND ⋮ SUBCOMPACT CARDINALS, TYPE OMISSION, AND LADDER SYSTEMS ⋮ TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS ⋮ The tree property and the continuum function below ⋮ Strong independence and its spectrum ⋮ The special Aronszajn tree property ⋮ Perfect subtree property for weakly compact cardinals ⋮ Diagonal supercompact Radin forcing ⋮ Set-theoretic geology ⋮ Successive failures of approachability

Cites Work

• Aronszajn trees and the successors of a singular cardinal
• Indestructible strong compactness but not supercompactness
• Fragility and indestructibility of the tree property
• On the consistency strength of the proper forcing axiom
• Adding closed unbounded subsets of \(\omega_2\) with finite forcing
• On the Hamkins approximation property
• Aronszajn trees on \(\aleph_2\) and \(\aleph_3\).
• The tree property at successors of singular cardinals
• The tree property
• Walks on ordinals and their characteristics
• The tree property at ℵ_ω+1
• THE TREE PROPERTY UP TO א_ω+1
• ARONSZAJN TREES AND FAILURE OF THE SINGULAR CARDINAL HYPOTHESIS
• Superdestructibility: A dual to Laver's indestructibility
• A very weak square principle
• Small forcing makes any cardinal superdestructible
• Aronszajn trees and the independence of the transfer property
• The fine structure of the constructible hierarchy
• Some combinatorial problems concerning uncountable cardinals
• Gap forcing

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