Cofinality of the partial ordering of functions from ω1 into ω under eventual domination

Thomas Jech; Karel Prikry

doi:10.1017/S0305004100061272

Cofinality of the partial ordering of functions from ω₁ into ω under eventual domination

Thomas Jech, Karel Prikry

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

It is unknown whether there can exist a family of functions from ω₁ into ω of size less than 2^N₁that dominates all functions fromω1 Intoω. 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.

Original language	English (US)
Pages (from-to)	25-32
Number of pages	8
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	95
Issue number	1
DOIs	https://doi.org/10.1017/S0305004100061272
State	Published - Jan 1984

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abstract = "It is unknown whether there can exist a family of functions from ω1 into ω of size less than 2N1 that dominates all functions fromω1 Intoω. 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.",

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