The consistency strength of choiceless failures of SCH

DOI10.2178/JSL/1278682215zbMath1202.03056OpenAlexW2159847132MaRDI QIDQ4931106

Arthur W. Apter, Peter Koepke

Publication date: 4 October 2010

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.533.1479

zbMATH Keywords

core modelsingular cardinals hypothesissymmetric inner modelSCHparallel Prikry forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35) Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55) Axiom of choice and related propositions (03E25)

Cites Work

• Unnamed Item
• The negation of the singular cardinal hypothesis from \(o(\kappa)=\kappa ^{++}\)
• Blowing up power of a singular cardinal -- wider gaps
• The strength of the failure of the singular cardinal hypothesis
• The consistency strength of \(\aleph_\omega\) and \(\aleph_{\omega_1}\) being Rowbottom cardinals without the axiom of choice
• The core model
• Powers of regular cardinals
• Indiscernible sequences for extenders, and the singular cardinal hypothesis

Related Items (2)

Violating the singular cardinals hypothesis without large cardinals ⋮ On weak square, approachability, the tree property, and failures of SCH in a choiceless context

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