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 Script error: No such module "Footnotes"..
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 Script error: No such module "Footnotes".. An inaccessible reflecting cardinal is not in general Mahlo however, see https://mathoverflow.net/q/212597.
See also
Bibliography
<templatestyles src="Refbegin/styles.css" />
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".