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

Thomas Jech, Karel Prikry

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)25-32
Number of pages8
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
StatePublished - Jan 1984

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