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Stationary Cardinals

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This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏ 11 -indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a∏ 11 -indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent of that of a stationary cardinal. As applications, we will show thatV=L implies ◊ 1 κ holds if κ is∏ 11 -indescribable and so forth.

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Authors and Affiliations

  1. Salem College, 27108, Winston-Salem, NC, USA

    Wenzhi Sun

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  1. Wenzhi Sun
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Sun, W. Stationary Cardinals. Arch Math Logic 32, 429–442 (1993). https://doi.org/10.1007/BF01270466

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  • DOI: https://doi.org/10.1007/BF01270466

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