Specializing Aronszajn Trees and Preserving Some Weak Diamonds

DOI10.1515/JAA.2009.47zbMath1183.03033OpenAlexW2134171732MaRDI QIDQ3399035

Heike Mildenberger, Saharon Shelah

Publication date: 29 September 2009

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jaa.2009.47

zbMATH Keywords

forcingweak diamondspecial Aronszajn treeindependence from ZFC

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05) Cardinal characteristics of the continuum (03E17)

Related Items (3)

Finding generic filters by playing games ⋮ SUBCOMPLETE FORCING, TREES, AND GENERIC ABSOLUTENESS ⋮ ARONSZAJN TREE PRESERVATION AND BOUNDED FORCING AXIOMS

Cites Work

• Random trees under CH
• There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
• A \({\Delta{}}^ 2_ 2\) well-order of the reals and incompactness of \(L(Q^{MM})\)
• A weak version of \(\lozenge\) which follows from \(2^{\aleph_0}<2^{\aleph_1}\)
• Creatures on ω₁ and weak diamonds
• Adding a closed unbounded set
• Parametrized $\diamondsuit $ principles
• The fine structure of the constructible hierarchy

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