ARONSZAJN TREES AND FAILURE OF THE SINGULAR CARDINAL HYPOTHESIS

DOI10.1142/S021906130900080XzbMath1204.03050MaRDI QIDQ3583041

Itay Neeman

Publication date: 26 August 2010

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

zbMATH Keywords

supercompact cardinalssingular cardinal hypothesistree propertyAronszajn trees

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05)

Related Items

A general tool for consistency results related to I1 ⋮ The tree property at ℵ_ω+1 ⋮ The tree property at ℵ_ω+1 ⋮ THE TREE PROPERTY UP TO א_ω+1 ⋮ Aronszajn trees and the successors of a singular cardinal ⋮ THE TREE PROPERTY AT AND ⋮ Piece selection and cardinal arithmetic ⋮ STATIONARY REFLECTION AND THE FAILURE OF THE SCH ⋮ On weak square, approachability, the tree property, and failures of SCH in a choiceless context ⋮ The tree property and the failure of SCH at uncountable cofinality ⋮ Forcing with sequences of models of two types ⋮ The ineffable tree property and failure of the singular cardinals hypothesis ⋮ Singularizing cardinals ⋮ Fragility and indestructibility. II ⋮ The tree property at the first and double successors of a singular ⋮ The definable tree property for successors of cardinals ⋮ I0 and rank-into-rank axioms ⋮ THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL ⋮ The tree property at the successor of a singular limit of measurable cardinals ⋮ Diagonal supercompact Radin forcing ⋮ The strong tree property and the failure of SCH ⋮ The tree property at the \(\aleph_{2 n}\)'s and the failure of SCH at \(\aleph_\omega\) ⋮ Successive failures of approachability ⋮ The tree property at first and double successors of singular cardinals with an arbitrary gap ⋮ Two-cardinal versions of weak compactness: partitions of triples

Cites Work

• Unnamed Item
• Shelah's pcf theory and its applications
• Some problems in singular cardinals combinatorics
• The negation of the singular cardinal hypothesis from \(o(\kappa)=\kappa ^{++}\)
• On the singular cardinals problem. I
• On the singular cardinals problem. II
• The tree property at successors of singular cardinals
• Canonical structure in the universe of set theory. I
• Combinatorial principles in the core model for one Woodin cardinal
• Blowing up the power of a singular cardinal
• The strength of the failure of the singular cardinal hypothesis
• Canonical structure in the universe of set theory. II.
• SQUARES, SCALES AND STATIONARY REFLECTION
• Cardinal Arithmetic
• The core model for sequences of measures. I
• Cardinal arithmetic for skeptics
• Extender based forcings
• A very weak square principle
• Singular Cardinals and the PCF Theory
• On SCH and the approachability property
• The proper forcing axiom and the singular cardinal hypothesis
• A model for a very good scale and a bad scale