Indestructibility of some compactness principles over models of \(\mathsf{PFA} \)

DOI10.1016/j.apal.2023.103359arXiv2208.02684OpenAlexW4386295579MaRDI QIDQ6050170

Šárka Stejskalová, Radek Honzík, Chris Lambie-Hanson

Publication date: 12 October 2023

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

Full work available at URL: https://arxiv.org/abs/2208.02684

zbMATH Keywords

indestructibilitytree propertyguessing modelsweak Kurepa hypothesis\( \mathsf{PFA} \)

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other set-theoretic hypotheses and axioms (03E65) Generic absoluteness and forcing axioms (03E57)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Guessing models and generalized Laver diamond
• The combinatorial essence of supercompactness
• Fragility and indestructibility of the tree property
• On the consistency strength of the proper forcing axiom
• Results on the generic Kurepa hypothesis
• A cofinality-preserving small forcing may introduce a special Aronszajn tree
• Aronszajn trees on \(\aleph_2\) and \(\aleph_3\).
• Some consequences of MA + non wKH
• The tree property at successors of singular cardinals
• Can a small forcing create Kurepa trees
• Small \(\mathfrak{u}(\kappa )\) at singular \(\kappa\) with compactness at \(\kappa^{++}\)
• QUOTIENTS OF STRONGLY PROPER FORCINGS AND GUESSING MODELS
• The tree property at ℵ_ω+2
• Approachability at the second successor of a singular cardinal
• Perfect-set forcing for uncountable cardinals
• Combinatorial Characterization of Supercompact Cardinals
• THE TREE PROPERTY AT AND
• THE EIGHTFOLD WAY
• INDESTRUCTIBILITY OF THE TREE PROPERTY
• The tree property at $\aleph _{\omega +2}$ with a finite gap
• Guessing models and the approachability ideal
• DESTRUCTIBILITY OF THE TREE PROPERTY AT ${\aleph _{\omega + 1}}$
• Guessing models imply the singular cardinal hypothesis
• Indestructible guessing models and the continuum
• Aronszajn trees and the independence of the transfer property
• Some combinatorial problems concerning uncountable cardinals
• TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS