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

  • Thomas Jech (a1) and Karel Prikry (a2)

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.

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

  • Thomas Jech (a1) and Karel Prikry (a2)

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