Omega-measurable cardinal
= Omega-measurable cardinal
{title2=$\omega\text{-measurable}$}
A cardinal is omega-measurable if it carries a <countably complete ultrafilter> that is a <nonprincipal ultrafilter>. Countable completeness rules out countable underlying sets. Such a measure is weaker than the cardinal's own full completeness requirement, but the <least omega-measurable cardinal is measurable>.