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

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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/s0168-0072(98)00011-6
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 69,043
Through your library

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.

Add more references

Citations of this work BETA

An Extension of Shelah’s Trichotomy Theorem.Shehzad Ahmed - 2019 - Archive for Mathematical Logic 58 (1-2):137-153.
Fallen Cardinals.Menachem Kojman & Saharon Shelah - 2001 - Annals of Pure and Applied Logic 109 (1-2):117-129.

Add more citations

Similar books and articles

More About Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1983 - Journal of Symbolic Logic 48 (2):441-457.
Exact Bounds for Lengths of Reductions in Typed Λ-Calculus.Arnold Beckmann - 2001 - Journal of Symbolic Logic 66 (3):1277-1285.
Low Upper Bounds of Ideals.Antonín Kučera & Theodore A. Slaman - 2009 - Journal of Symbolic Logic 74 (2):517-534.
Bounds for Covering Numbers.Andreas Liu - 2006 - Journal of Symbolic Logic 71 (4):1303 - 1310.
Low Upper Bounds in the LR Degrees.David Diamondstone - 2012 - Annals of Pure and Applied Logic 163 (3):314-320.
Upper Bounds for the Arithmetical Degrees.M. Lerman - 1985 - Annals of Pure and Applied Logic 29 (3):225-254.
Minimal Upper Bounds for Arithmetical Degrees.Masahiro Kumabe - 1994 - Journal of Symbolic Logic 59 (2):516-528.


Added to PP index

Total views
10 ( #896,026 of 2,498,734 )

Recent downloads (6 months)
1 ( #426,098 of 2,498,734 )

How can I increase my downloads?


My notes