AD and patterns of singular cardinals below Θ

DOI10.2307/2275606zbMath0855.03029OpenAlexW1590233520MaRDI QIDQ4879909

Arthur W. Apter

Publication date: 9 February 1997

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

Full work available at URL: https://doi.org/10.2307/2275606

zbMATH Keywords

forcinginner modelaxiom of determinacycofinality functionrelative consistency result

Mathematics Subject Classification ID

Consistency and independence results (03E35) Determinacy principles (03E60)

Related Items (8)

The first measurable cardinal can be the first uncountable regular cardinal at any successor height ⋮ Controlling the number of normal measures at successor cardinals ⋮ Consecutive singular cardinals and the continuum function ⋮ Cofinality and measurability of the first three uncountable cardinals ⋮ On the consistency strength of two choiceless cardinal patterns ⋮ The consistency strength of \(\aleph_\omega\) and \(\aleph_{\omega_1}\) being Rowbottom cardinals without the axiom of choice ⋮ The calculus of partition sequences, changing cofinalities, and a question of Woodin ⋮ The strength of choiceless patterns of singular and weakly compact cardinals

Cites Work

• On a problem inspired by determinacy
• Descriptive set theory
• All uncountable cardinals can be singular
• Cabal seminar 77 -- 79. Proceedings, Caltech-UCLA Logic Seminar 1977 -- 79
• Some new upper bounds in consistency strength for certain choiceless large cardinal patterns
• Measurable cardinals and the continuum hypothesis
• The axiom of determinacy implies dependent choices in L(R)
• Projective determinacy
• Strong axioms of infinity and elementary embeddings
• Ad “the κn are Jonsson cardinals and κω is a Rowbottom cardinal”
• Some strong axioms of infinity incompatible with the axiom of constructibility

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