Large cardinals with few measures

DOI10.1090/S0002-9939-07-08786-2zbMath1115.03075arXivmath/0603260MaRDI QIDQ3432792

Arthur W. Apter, James Cummings, Joel David Hamkins

Publication date: 18 April 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603260

zbMATH Keywords

strongly compact cardinalmeasurable cardinalsupercompact cardinalnormal measure

Mathematics Subject Classification ID

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

Related Items (10)

Coding into HOD via normal measures with some applications ⋮ The structure of the Mitchell order. I ⋮ HOD-supercompactness, Indestructibility, and Level by Level Equivalence ⋮ Controlling the number of normal measures at successor cardinals ⋮ Forcing Magidor iteration over a core model below \(0^P\) ⋮ The structure of the Mitchell order. II. ⋮ Indestructibility and measurable cardinals with few and many measures ⋮ JOINT DIAMONDS AND LAVER DIAMONDS ⋮ Many normal measures ⋮ Normal measures on large cardinals

Cites Work

• Possible behaviours for the Mitchell ordering
• Measurable cardinals and the continuum hypothesis
• The lottery preparation
• Some Remarks on Normal Measures and Measurable Cardinals
• Identity crises and strong compactness
• The ⊲-ordering on normal ultrafilters
• Sets constructible from sequences of ultrafilters
• How large is the first strongly compact cardinal? or a study on identity crises
• Superdestructibility: A dual to Laver's indestructibility
• Small forcing makes any cardinal superdestructible
• Set Theory
• Extensions with the approximation and cover properties have no new large cardinals
• Boolean extensions and measurable cardinals
• Some applications of iterated ultrapowers in set theory
• Gap forcing

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