The tree property
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Publication:1380329
DOI10.1006/aima.1997.1680zbMath0949.03039OpenAlexW2092835503WikidataQ29400138 ScholiaQ29400138MaRDI QIDQ1380329
James Cummings, Matthew Foreman
Publication date: 6 December 2000
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/aima.1997.1680
Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05)
Related Items (39)
THE TREE PROPERTY UP TO אω+1 ⋮ Aronszajn trees and the successors of a singular cardinal ⋮ THE TREE PROPERTY AT AND ⋮ The super tree property at the successor of a singular ⋮ The tree property at double successors of singular cardinals of uncountable cofinality ⋮ INDESTRUCTIBILITY OF THE TREE PROPERTY ⋮ TREES AND STATIONARY REFLECTION AT DOUBLE SUCCESSORS OF REGULAR CARDINALS ⋮ The strong tree property and weak square ⋮ The tree property and the continuum function below ⋮ The tree property below \(\aleph_{\omega \cdot 2}\) ⋮ A remark on the tree property in a choiceless context ⋮ The tree property at the double successor of a singular cardinal with a larger gap ⋮ Fragility and indestructibility of the tree property ⋮ Strong tree properties for two successive cardinals ⋮ The ineffable tree property and failure of the singular cardinals hypothesis ⋮ A Laver-like indestructibility for hypermeasurable cardinals ⋮ The tree property at $\aleph _{\omega +2}$ with a finite gap ⋮ Fragility and indestructibility. II ⋮ THE EIGHTFOLD WAY ⋮ The tree property at the first and double successors of a singular ⋮ The tree property at ℵω+2 ⋮ The definable tree property for successors of cardinals ⋮ Guessing models and the approachability ideal ⋮ THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL ⋮ Strong tree properties for small cardinals ⋮ The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps ⋮ Diagonal supercompact Radin forcing ⋮ The strong tree property and the failure of SCH ⋮ Cellularity and the structure of pseudo-trees ⋮ More on full reflection below \({\aleph_\omega}\) ⋮ Easton's theorem for the tree property below \(\aleph_\omega\) ⋮ Laver and set theory ⋮ The tree property at the \(\aleph_{2 n}\)'s and the failure of SCH at \(\aleph_\omega\) ⋮ Successive failures of approachability ⋮ A model of Cummings and Foreman revisited ⋮ Some applications of mixed support iterations ⋮ The tree property at first and double successors of singular cardinals with an arbitrary gap ⋮ ITP, ISP, AND SCH ⋮ The tree property at both ℵω+1and ℵω+2
Cites Work
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- Aronszajn trees on \(\aleph_2\) and \(\aleph_3\).
- Set theory. An introduction to independence proofs
- Proper forcing
- Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
- The generalized continuum hypothesis can fail everywhere
- Between Martin's Axiom and Souslin's Hypothesis
- Aronszajn trees and the independence of the transfer property
- On sequences generic in the sense of Prikry
- Sur un problème de Sikorski
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