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- Unfoldable_cardinal abstract "In mathematics, an unfoldable cardinal is a certain kind of large cardinal number.Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j(κ) ≥ λ.A cardinal is unfoldable if and only if it is an λ-unfoldable for all ordinals λ.A cardinal number κ is strongly λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model "N" with the critical point of j being κ, j(κ) ≥ λ, and V(λ) is a subset of N. Without loss of generality, we can demand also that N contains all its sequences of length λ.Likewise, a cardinal is strongly unfoldable if and only if it is strongly λ-unfoldable for all λ.These properties are essentially weaker versions of strong and supercompact cardinals, consistent with V = L. Many theorems related to these cardinals have generalizations to their unfoldable or strongly unfoldable counterparts. For example, the existence of a strongly unfoldable implies the consistency of a slightly weaker version of the proper forcing axiom.A Ramsey cardinal is unfoldable, and will be strongly unfoldable in L. It may fail to be strongly unfoldable in V, however.In L, any unfoldable cardinal is strongly unfoldable; thus unfoldables and strongly unfoldables have the same consistency strength.A cardinal k is κ-strongly unfoldable, and κ-unfoldable, if and only if it is weakly compact. A κ+ω-unfoldable cardinal is totally indescribable and preceded by a stationary set of totally indescribable cardinals.".
- Unfoldable_cardinal wikiPageExternalLink 0409304).
- Unfoldable_cardinal wikiPageID "853783".
- Unfoldable_cardinal wikiPageLength "2949".
- Unfoldable_cardinal wikiPageOutDegree "28".
- Unfoldable_cardinal wikiPageRevisionID "624253226".
- Unfoldable_cardinal wikiPageWikiLink Axiom_of_constructibility.
- Unfoldable_cardinal wikiPageWikiLink Cardinal_number.
- Unfoldable_cardinal wikiPageWikiLink Category:Large_cardinals.
- Unfoldable_cardinal wikiPageWikiLink Consistency_strength.
- Unfoldable_cardinal wikiPageWikiLink Critical_point_(set_theory).
- Unfoldable_cardinal wikiPageWikiLink Elementary_embedding.
- Unfoldable_cardinal wikiPageWikiLink Elementary_equivalence.
- Unfoldable_cardinal wikiPageWikiLink Equiconsistency.
- Unfoldable_cardinal wikiPageWikiLink Indescribable_cardinal.
- Unfoldable_cardinal wikiPageWikiLink Inner_model.
- Unfoldable_cardinal wikiPageWikiLink J._Symbolic_Logic.
- Unfoldable_cardinal wikiPageWikiLink Joel_David_Hamkins.
- Unfoldable_cardinal wikiPageWikiLink Journal_of_Symbolic_Logic.
- Unfoldable_cardinal wikiPageWikiLink Large_cardinal.
- Unfoldable_cardinal wikiPageWikiLink Mathematics.
- Unfoldable_cardinal wikiPageWikiLink Ordinal_number.
- Unfoldable_cardinal wikiPageWikiLink Power_set.
- Unfoldable_cardinal wikiPageWikiLink Proper_forcing_axiom.
- Unfoldable_cardinal wikiPageWikiLink Ramsey_cardinal.
- Unfoldable_cardinal wikiPageWikiLink Strong_cardinal.
- Unfoldable_cardinal wikiPageWikiLink Supercompact_cardinal.
- Unfoldable_cardinal wikiPageWikiLink The_Journal_of_Symbolic_Logic.
- Unfoldable_cardinal wikiPageWikiLink Totally_indescribable_cardinal.
- Unfoldable_cardinal wikiPageWikiLink Weakly_compact_cardinal.
- Unfoldable_cardinal wikiPageWikiLink ZFC.
- Unfoldable_cardinal wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Unfoldable_cardinal wikiPageWikiLinkText "Unfoldable cardinal".
- Unfoldable_cardinal wikiPageWikiLinkText "unfoldable cardinal".
- Unfoldable_cardinal wikiPageWikiLinkText "unfoldable".
- Unfoldable_cardinal wikiPageWikiLinkText "λ-unfoldable".
- Unfoldable_cardinal hasPhotoCollection Unfoldable_cardinal.
- Unfoldable_cardinal wikiPageUsesTemplate Template:Doi.
- Unfoldable_cardinal wikiPageUsesTemplate Template:Settheory-stub.
- Unfoldable_cardinal subject Category:Large_cardinals.
- Unfoldable_cardinal hypernym Kind.
- Unfoldable_cardinal comment "In mathematics, an unfoldable cardinal is a certain kind of large cardinal number.Formally, a cardinal number κ is λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model with the critical point of j being κ and j(κ) ≥ λ.A cardinal is unfoldable if and only if it is an λ-unfoldable for all ordinals λ.A cardinal number κ is strongly λ-unfoldable if and only if for every transitive model M of cardinality κ of ZFC-minus-power set such that κ is in M and M contains all its sequences of length less than κ, there is a non-trivial elementary embedding j of M into a transitive model "N" with the critical point of j being κ, j(κ) ≥ λ, and V(λ) is a subset of N. ".
- Unfoldable_cardinal label "Unfoldable cardinal".
- Unfoldable_cardinal sameAs m.03hdgh.
- Unfoldable_cardinal sameAs Q7884364.
- Unfoldable_cardinal sameAs Q7884364.
- Unfoldable_cardinal wasDerivedFrom Unfoldable_cardinal?oldid=624253226.
- Unfoldable_cardinal isPrimaryTopicOf Unfoldable_cardinal.