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 {{harv|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 {{harv|Mekler|Shelah|1989}}. An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.