Annals of Pure and Applied Logic 92 (3):267-282 (1998)

Abstract
The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem gives a necessary and sufficient condition for the existence of an exact upper bound ƒ for a ¦A¦+ is regular: an eub ƒ with lim infI cf ƒ = μ exists if and only if for every regular κ ε the set of flat points in tf of cofinality κ is stationary. Two applications of the main Theorem to set theory are presented. A theorem of Magidor's on covering between models of ZFC is proved using the main theorem : If V-W are transitive models of set theory with ω-covering and GCH holds in V, then κ-covering holds between V and W for all cardinals κ. A new proof of a Theorem by Cummings on collapsing successors of singulars is also given . The appendix to the paper contains a short proof of Shelah's trichotomy theorem, for the reader's convenience
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DOI 10.1016/s0168-0072(98)00011-6
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References found in this work BETA

Shelah's Pcf Theory and its Applications.Maxim R. Burke & Menachem Magidor - 1990 - Annals of Pure and Applied Logic 50 (3):207-254.

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