In set theory, a mathematical discipline, a reflecting cardinal is a cardinal number ú for which there is a normal ideal I on ú such that for every XâÂÂI<sup>+</sup>, the set of ñâÂÂú for which X reflects at ñ is in I<sup>+</sup>. (A stationary subset S of ú is said to reflect at ñ<ú if Sâ©ñ is stationary in ñ.) Reflecting cardinals were introduced by .
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 ú is called greatly Mahlo if it is ú<sup>+</sup>-Mahlo . An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.