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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Detalles Bibliográficos
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:	Cardinal numbers ASCII (Character set) Transfinite numbers Set theory Character sets (Data processing) Mathematical logic
Acceso en línea:	Ver este registro en EBSCOhost

Descripción
Sumario:	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.