Small forcing creates neither strong nor Woodin cardinals

DOI10.1090/S0002-9939-00-05347-8zbMath0959.03040arXivmath/9808124MaRDI QIDQ4501093

W. Hugh Woodin, Joel David Hamkins

Publication date: 3 September 2000

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

Full work available at URL: https://arxiv.org/abs/math/9808124

zbMATH Keywords

large cardinalsstrong cardinalWoodin cardinalsmall forcingstrongness embedding

Mathematics Subject Classification ID

Large cardinals (03E55) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (18)

Identity crises and strong compactness. III: Woodin cardinals ⋮ Exactly controlling the non-supercompact strongly compact cardinals ⋮ The least strongly compact can be the least strong and indestructible ⋮ Preserving levels of projective determinacy by tree forcings ⋮ Easton's theorem in the presence of Woodin cardinals ⋮ Unnamed Item ⋮ Choiceless Ramsey theory of linear orders ⋮ Continuity of coordinate functionals of filter bases in Banach spaces ⋮ On tall cardinals and some related generalizations ⋮ On some properties of Shelah cardinals ⋮ Certain very large cardinals are not created in small forcing extensions ⋮ Supercompactness and measurable limits of strong cardinals ⋮ Regular embeddings of the stationary tower and Woodin's maximality theorem ⋮ Gap forcing ⋮ A note on tall cardinals and level by level equivalence ⋮ Set-theoretic geology ⋮ Incompatible Ω-Complete Theories ⋮ Tall cardinals

Cites Work

• Measurable cardinals and the continuum hypothesis

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