All uncountable cardinals can be singular

DOI10.1007/BF02760939zbMath0439.03036MaRDI QIDQ1142208

M. B. Gitik

Publication date: 1980

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

singular cardinalsuncountable cardinals

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55)

Related Items (28)

Partition properties and Prikry forcing on simple spaces ⋮ Changing cofinalities and the nonstationary ideal ⋮ On a problem inspired by determinacy ⋮ Spaces of Urelements. II ⋮ The first measurable cardinal can be the first uncountable regular cardinal at any successor height ⋮ Two new algebraic equivalents to the axiom of choice ⋮ Choiceless Ramsey theory of linear orders ⋮ Sequential and distributive forcings without choice ⋮ Measurable cardinals and choiceless axioms ⋮ A class of higher inductive types in Zermelo‐Fraenkel set theory ⋮ Remarks on Gitik's model and symmetric extensions on products of the Lévy collapse ⋮ Consecutive singular cardinals and the continuum function ⋮ Fodor's lemma can fail everywhere ⋮ Extending compact topologies to compact Hausdorff topologies in \(\mathbf {ZF}\) ⋮ AD and patterns of singular cardinals below Θ ⋮ Canonical seeds and Prikry trees ⋮ Asymptotic Quasi-completeness and ZFC ⋮ The weak choice principle WISC may fail in the category of sets ⋮ Making all cardinals almost Ramsey ⋮ A new characterization of supercompactness and applications ⋮ Unnamed Item ⋮ Semantics of higher inductive types ⋮ On the class of measurable cardinals without the axiom of choice ⋮ The Morris model ⋮ All uncountable cardinals in the Gitik model are almost Ramsey and carry Rowbottom filters ⋮ The strength of choiceless patterns of singular and weakly compact cardinals ⋮ Polarized relations at singulars over successors ⋮ Choiceless Löwenheim-Skolem property and uniform definability of grounds

Cites Work

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• Lectures in set theory with particular emphasis on the method of forcing
• Zur Axiomatik der Mengenlehre (Fundierungs‐ und Auswahlaxiom)
• The core model
• Comparison of the axioms of local and universal choice

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