Reflecting cardinal

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 X∈I⁺, 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. Every reflecting cardinal is a greatly Mahlo cardinal, and is also a limit of greatly Mahlo cardinals, where a cardinal κ is called greatly Mahlo if it is κ⁺-Mahlo.