A POLARIZED PARTITION RELATION FOR WEAKLY COMPACT CARDINALS USING ELEMENTARY SUBSTRUCTURES.
We show that if κ isa weakly compact cardinal, then (Multiple line equation(s) cannot be represented in ASCII text) for any ordinals α κ κand μ < κ, and any finite ordinals m and n. This polarized partition relation represents the statement that for any partition κ X κ = ∪ K U ∪ L of κ x κ into m +...
| Publicado en: | Journal of Symbolic Logic Vol. 71; no. 4; pp. 1342 - 1353 |
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| Formato: | Artículo |
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Cambridge University Press
Dec2006
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=23334459&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 23334459 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Dec2006 vid: 71 iid: 4 pid: 15979 pub: Cambridge University Press artinfo: ui: 23334459 10.2178/jsl/1164060459 ppf: 1342 ppct: 11 formats: tig: atl: A POLARIZED PARTITION RELATION FOR WEAKLY COMPACT CARDINALS USING ELEMENTARY SUBSTRUCTURES. aug: au: Jones, Albin L. affil: Department of Mathematics, University of Kansas, Lawrence, KS 66045-2142, USA su: Cardinal numbers ASCII (Character set) Transfinite numbers Set theory Character sets (Data processing) Mathematical logic sug: subj: Cardinal numbers ASCII (Character set) Transfinite numbers Set theory Character sets (Data processing) Mathematical logic ab: We show that if κ isa weakly compact cardinal, then (Multiple line equation(s) cannot be represented in ASCII text) for any ordinals α κ κand μ < κ, and any finite ordinals m and n. This polarized partition relation represents the statement that for any partition κ X κ = ∪ K U ∪ L of κ x κ into m + μ pieces either there are A ϵ [κ], B ϵ [κ], and i < m with A x B ⊆ K or there are C ϵ [κ], D ϵ [κ], and j < μ with C x D ⊆ L. Related results for measurable and almost measurable κ are also investigated. Our proofs of these relations involve the use of elementary substructures of set models of large fragments of ZFC. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2006 holdings: @attributes: islocal: N |
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