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+.
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 κ is called greatly Mahlo if it is κ+-Mahlo. An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.
