Creatures on ω1 and weak diamonds

DOI10.2178/jsl/1231082299zbMath1193.03075OpenAlexW2157627761MaRDI QIDQ3616340

Heike Mildenberger

Publication date: 25 March 2009

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1231082299

zbMATH Keywords

coveringdominating numbercountable support iterationAronszajn treecreature forcingbounding numberSuslin treeparametrized diamond principles

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Cardinal characteristics of the continuum (03E17)

Related Items (2)

Finding generic filters by playing games ⋮ Specializing Aronszajn Trees and Preserving Some Weak Diamonds

Cites Work

• Random trees under CH
• Sheva-sheva-sheva: large creatures
• There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
• Specialising Aronszajn trees by countable approximations
• Measured creatures
• Iterated perfect-set forcing
• Norms on possibilities. I. Forcing with trees and creatures
• Parametrized $\diamondsuit $ principles
• The fine structure of the constructible hierarchy
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