Israel Journal of Mathematics

, Volume 67, Issue 3, pp 353–366

The consistency strength of “every stationary set reflects”

  • Alan H. Mekler
  • Saharon Shelah

DOI: 10.1007/BF02764953

Cite this article as:
Mekler, A.H. & Shelah, S. Israel J. Math. (1989) 67: 353. doi:10.1007/BF02764953


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).

Copyright information

© The Weizmann Science Press of Israel 1989

Authors and Affiliations

  • Alan H. Mekler
    • 1
  • Saharon Shelah
    • 2
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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