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The consistency strength of “every stationary set reflects”

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Abstract

The consistency strength of a regular cardinal so that every stationary set reflects is the same as that of a regular cardinal with a normal idealI so that everyI-positive set reflects in aI-positive set. We call such a cardinal areflection cardinal and such an ideal areflection ideal. The consistency strength is also the same as the existence of a regular cardinal κ so that every κ-free (abelian) group is κ+-free. In L, the first reflection cardinal is greater than the first greatly Mahlo cardinal and less than the first weakly compact cardinal (if any).

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Alan H. Mekler

  2. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

Authors
  1. Alan H. Mekler
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  2. Saharon Shelah
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Additional information

Research supported by NSERC grant # A8948.

Publication # 367. Research partially supported by the BSF.

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Mekler, A.H., Shelah, S. The consistency strength of “every stationary set reflects”. Israel J. Math. 67, 353–366 (1989). https://doi.org/10.1007/BF02764953

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  • DOI: https://doi.org/10.1007/BF02764953

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