Iterable cardinal
In mathematics, an iterable cardinal is a type of large cardinal introduced by, and, and further studied by. Sharpe and Welch defined a cardinal κ to be iterable if every subset of κ is contained in a weak κ-model M for which there exists an M-ultrafilter on κ which allows for wellfounded iterations by ultrapowers of arbitrary length.
Gitman gave a finer notion, where a cardinal κ is defined to be α-iterable
if ultrapower iterations only of length α are required to wellfounded.
