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γ-ramsey and γ-ineffable cardinals

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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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Authors and Affiliations

  1. Department of Mathematics, Smith College, 01060, Northampton, Mass., USA

    James M. Henle

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  1. James M. Henle
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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

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