Carnegie Mellon University
Browse

Exact upper bounds and their uses in set theory

Download (2.06 MB)
journal contribution
posted on 1997-01-01, 00:00 authored by Menachem Kojman
Abstract: "The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem (Theorem 18 below) gives a necessary and sufficient condition for the existence of an exact upper bound f for a <[subscript I]-increasing sequence f̄ = [f[subscript α] : α < [lambda]] [subset] On[superscript A] where [lambda] > [absolute value of A]⁺ is regular: an eub f with lim inf[subscript I]cf f(a) = [mu] exists if and only if for every regular k [element of] ([absolute value A], [mu]) the set of flat points in f̄ of cofinality k 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 (Theorem 22): If V [element of] W are transitive models of set theory with [omega]-covering and GCH holds in V, then k-covering holds between V and W for all cardinals k. A new proof of a theorem by Cummings on collapsing successors of singulars is also given (Theorem 24). The appendix to the paper contains a short proof of Shelah's trichotomy theorem, for the reaser's [sic] convenience."

History

Publisher Statement

All Rights Reserved

Date

1997-01-01

Usage metrics

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC