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Cofinality of the partial ordering of functions from Ω1 into Ω under eventual domination

Published online by Cambridge University Press:  24 October 2008

Thomas Jech  and
Karel Prikry
Thomas Jech
Affiliation:
Pennsylvania State University
Karel Prikry
Affiliation:
University of Minnesota
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Abstract

It is unknown whether there can exist a family of functions from Ω1 into Ω of size less than that dominates all functions from Ω1 into Ω. We show that there is no such family if the continuum is real-valued measurable, and that the existence of such a family has consequences for cardinal arithmetic, and is related to large cardinal axioms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 25 - 32
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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