On the strong equality between supercompactness and strong compactness
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Publication:5690966
DOI10.1090/S0002-9947-97-01531-6zbMath0864.03036arXivmath/9502232OpenAlexW1522767951MaRDI QIDQ5690966
Arthur W. Apter, Saharon Shelah
Publication date: 9 January 1997
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9502232
Related Items (37)
Exactly controlling the non-supercompact strongly compact cardinals ⋮ Failures of SCH and level by level equivalence ⋮ INDESTRUCTIBILITY WHEN THE FIRST TWO MEASURABLE CARDINALS ARE STRONGLY COMPACT ⋮ Patterns of compact cardinals ⋮ Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness ⋮ On the consistency strength of level by level inequivalence ⋮ HOD-supercompactness, Indestructibility, and Level by Level Equivalence ⋮ Precisely controlling level by level behavior ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ A note on the normal filters extension property ⋮ Some structural results concerning supercompact cardinals ⋮ Menas’ Result is Best Possible ⋮ Capturing sets of ordinals by normal ultrapowers ⋮ Strong combinatorial principles and level by level equivalence ⋮ Level by level inequivalence beyond measurability ⋮ Identity crises and strong compactness ⋮ More on HOD-supercompactness ⋮ The Ultrapower Axiom ⋮ An \(L\)-like model containing very large cardinals ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ Indestructibility and measurable cardinals with few and many measures ⋮ Supercompactness and measurable limits of strong cardinals ⋮ Inaccessible cardinals, failures of GCH, and level-by-level equivalence ⋮ Diamond, square, and level by level equivalence ⋮ Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions ⋮ A note on tall cardinals and level by level equivalence ⋮ Large cardinals and locally defined well-orders of the universe ⋮ Strongly compact cardinals and the continuum function ⋮ Forcing the Least Measurable to Violate GCH ⋮ Indestructibility under adding Cohen subsets and level by level equivalence ⋮ Partial strong compactness and squares ⋮ Tallness and level by level equivalence and inequivalence ⋮ Indestructibility, measurability, and degrees of supercompactness ⋮ Indestructible strong compactness and level by level inequivalence ⋮ A universal indestructibility theorem compatible with level by level equivalence ⋮ Normal measures on large cardinals ⋮ Indestructibility and the level-by-level agreement between strong compactness and supercompactness
Cites Work
- On the least strongly compact cardinal
- There are many normal ultrafilters corresponding to a supercompact cardinal
- 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
- How large is the first strongly compact cardinal? or a study on identity crises
- Strong axioms of infinity and elementary embeddings
- Menas’ Result is Best Possible
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