The strength of the failure of the singular cardinal hypothesis

DOI10.1016/0168-0072(91)90016-FzbMath0726.03036OpenAlexW2051800246MaRDI QIDQ2277450

M. B. Gitik

Publication date: 1991

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(91)90016-f

zbMATH Keywords

forcingsingular cardinalcardinal arithmeticCovering Lemma

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other set-theoretic hypotheses and axioms (03E65)

Related Items (32)

The secret life of \(\mu\)-clubs ⋮ Cardinal arithmetic for skeptics ⋮ Narrow coverings of \(\omega\)-ary product spaces ⋮ Possible values for \(2^{\aleph_n}\) and \(2^{\aleph_\omega}\) ⋮ More on the cut and choose game ⋮ Violating the singular cardinals hypothesis without large cardinals ⋮ Cardinal characteristics at \(\aleph_\omega\) ⋮ A framework for forcing constructions at successors of singular cardinals ⋮ Covering versus partitioning with Polish spaces ⋮ MENAS’S CONJECTURE REVISITED ⋮ Piece selection and cardinal arithmetic ⋮ Negating the Galvin property ⋮ The Borel partition spectrum at successors of singular cardinals ⋮ On minimal non-\(\sigma\)-scattered linear orders ⋮ Global singularization and the failure of SCH ⋮ Singular Cardinals and the PCF Theory ⋮ Kunen and set theory ⋮ Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics ⋮ Combinatorial aspects of selective star covering properties in \(\Psi\)-spaces ⋮ CLOSURE PROPERTIES OF MEASURABLE ULTRAPOWERS ⋮ On the Singular Cardinal Hypothesis ⋮ Diagonal supercompact Radin forcing ⋮ ARONSZAJN TREES AND FAILURE OF THE SINGULAR CARDINAL HYPOTHESIS ⋮ The consistency strength of choiceless failures of SCH ⋮ On the consistency strength of the Milner-Sauer conjecture ⋮ ON THE SPLITTING NUMBER AT REGULAR CARDINALS ⋮ Indiscernible sequences for extenders, and the singular cardinal hypothesis ⋮ Strongly compact cardinals and the continuum function ⋮ The character of topological groups, via bounded systems, Pontryagin-van Kampen duality and pcf theory ⋮ Changing cofinalities and collapsing cardinals in models of set theory ⋮ On gaps under GCH type assumptions ⋮ Normal measures on large cardinals

Cites Work

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• Shelah's pcf theory and its applications
• Changing cofinalities and the nonstationary ideal
• Successors of singulars, cofinalities of reduced products of cardinals and productivity of chain conditions
• On the Mitchell and Rudin-Keisler orderings of ultrafilters
• The negation of the singular cardinal hypothesis from \(o(\kappa)=\kappa ^{++}\)
• Proper forcing
• On the singular cardinals problem. I
• On the singular cardinals problem. II
• Products of regular cardinals and cardinal invariants of products of Boolean algebras
• Applications of the Covering Lemma for Sequences of Measures
• The core model for sequences of measures. I
• On the Singular Cardinal Hypothesis

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