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A Variation on a Theorem of Galvin and Hajnal
Author(s) -
Jech Thomas
Publication year - 1993
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/25.2.97
Subject(s) - cofinality , uncountable set , mathematics , regular cardinal , limit (mathematics) , discrete mathematics , combinatorics , norm (philosophy) , pure mathematics , mathematical analysis , countable set , political science , law
Let ℵ η be a singular cardinal of regular uncountable cofinality κ. Let {η(ξ): ξ < κ} be a continuous increasing sequence with limit η, and let κ ξ =ℵ η(ξ)+Ф(ξ) ,ξ < κ be regular cardinals. Let I be a normal ideal on κ, and assume that the reduced product ∏ ξ<κ κ ξ / I admits a cofinal λ‐scale of ordinal functions. Then λ ⩽ ℵ η+τ , where τ=∥Ф∥ I is the I ‐norm of Ф.