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Uniformization principles

Published online by Cambridge University Press:  12 March 2014

Alan H. Mekler
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Saharon Shelah
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel

Abstract

It is consistent that for many cardinals λ there is a family of at least λ+ unbounded subsets of λ which have uniformization properties. In particular if it is consistent that a supercompact cardinal exists, then it is consistent that ℵω has such a family. We have applications to point set topology, Whitehead groups and reconstructing separable abelian p-groups from their socles.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1989

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