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 +...

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Publicado en:Journal of Symbolic Logic Vol. 71; no. 4; pp. 1342 - 1353
Autor principal: Jones, Albin L.
Formato: Artículo
Publicado: Cambridge University Press Dec2006
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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      dt: Dec2006
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        atl: A POLARIZED PARTITION RELATION FOR WEAKLY COMPACT CARDINALS USING ELEMENTARY SUBSTRUCTURES.
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        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
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        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
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          year: 2006
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