# The consistency strength of “every stationary set reflects”

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DOI: 10.1007/BF02764953

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

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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 ideal*I* so that every*I*-positive set reflects in a*I*-positive set. We call such a cardinal a*reflection cardinal* and such an ideal a*reflection 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).