In mathematics, an iterable cardinal is a type of large cardinal introduced by , and , and further studied by . Sharpe and Welch defined a cardinal ú to be iterable if every subset of ú is contained in a weak ú-model M for which there exists an M-ultrafilter on ú which allows for wellfounded iterations by ultrapowers of arbitrary length. Gitman gave a finer notion, where a cardinal ú is defined to be ñ-iterable if ultrapower iterations only of length ñ are required to wellfounded. (By standard arguments iterability is equivalent to ÃÂ<sub>1</sub>-iterability.)