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A few remarks on Rowbottom cardinals

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Abstract

It is proved that every regular Rowbottom cardinal which is greater than the continuum is strongly inaccessible. We notice that the theory “ZFC + every cardinal of cofinality ω is Rowbottom” is inconsistent. This answers a question raised by C. C. Chang and H. J. Keisler.

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References

  1. C. C. Chang and H. J. Keisler,Model Theory, North-Holland Publ. Co., Amsterdam, 1973.

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  2. F. R. Drake,Set Theory, North-Holland Publ. Co., Amsterdam, 1974.

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  3. K. Prikry,Ideal and powers of cardinals, Bull. Amer. Math. Soc.81 (1975), 907–909.

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Authors and Affiliations

  1. Department of Mathematics, Gdańsk University, Wita Stwosza 57, 80952, Gdańsk, Poland

    Jan Tryba

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  1. Jan Tryba
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Tryba, J. A few remarks on Rowbottom cardinals. Israel J. Math. 40, 193–196 (1981). https://doi.org/10.1007/BF02761361

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  • DOI: https://doi.org/10.1007/BF02761361

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