In set theory, a mathematical discipline, a reflecting cardinal is a cardinal number κ for which there is a normal ideal I on κ such that for every XI+, the set of α∈κ for which X reflects at α is in I+. (A stationary subset S of κ is said to reflect at α<κ if S∩α is stationary in α.) Reflecting cardinals were introduced by (Mekler & Shelah 1989).

Every weakly compact cardinal is a reflecting cardinal, and is also a limit of reflecting cardinals. The consistency strength of an inaccessible reflecting cardinal is strictly greater than a greatly Mahlo cardinal, where a cardinal κ is called greatly Mahlo if it is κ+-Mahlo (Mekler & Shelah 1989). An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.

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