Menas’ Result is Best Possible

DOI10.1090/S0002-9947-97-01691-7zbMath0876.03030arXivmath/9512226MaRDI QIDQ4336552

Saharon Shelah, Arthur W. Apter

Publication date: 13 May 1997

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

Full work available at URL: https://arxiv.org/abs/math/9512226

zbMATH Keywords

strongly compact cardinalmeasurable cardinaliterated forcingsupercompact cardinal

Mathematics Subject Classification ID

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

Related Items (14)

Patterns of compact cardinals ⋮ Strong compactness and the ultrapower axiom I: the least strongly compact cardinal ⋮ Some structural results concerning supercompact cardinals ⋮ Capturing sets of ordinals by normal ultrapowers ⋮ Identity crises and strong compactness ⋮ On the strong equality between supercompactness and strong compactness ⋮ Group radicals and strongly compact cardinals ⋮ Supercompactness and measurable limits of strong cardinals ⋮ Inaccessible cardinals, failures of GCH, and level-by-level equivalence ⋮ JOINT DIAMONDS AND LAVER DIAMONDS ⋮ On measurable limits of compact cardinals ⋮ Forcing the Least Measurable to Violate GCH ⋮ Indestructibility, measurability, and degrees of supercompactness ⋮ Normal measures on large cardinals

Cites Work

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• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Measurable cardinals and the continuum hypothesis
• On the role of supercompact and extendible cardinals in logic
• A Model in Which GCH Holds at Successors but Fails at Limits
• On strong compactness and supercompactness
• Strong axioms of infinity and elementary embeddings
• Changing cofinality of cardinals
• On the strong equality between supercompactness and strong compactness

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