Abstract
A number of related combinatorial properties of a cardinal κ contradicting AC are examined. Chief results include: (1) For many ordinals γ, к → (к)γ implies к к (к)<γ. (2) For many ordinals γ, if к к (к) αγ for all α<κ, then κ is γ-weakly ineffable. (3) For all infinite cardinals γ, к к (к)<γ implies κ is <γ-weakly ineffable.
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Many of the results in this paper appeared originally in the author’s doctoral dissertation.
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Henle, J.M. γ-ramsey and γ-ineffable cardinals. Israel J. Math. 30, 85–98 (1978). https://doi.org/10.1007/BF02760831
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DOI: https://doi.org/10.1007/BF02760831