# Critical point (set theory)

If N is V, then κ (the critical point of j) is always a measurable cardinal, i.e. an uncountable cardinal number κ such that there exists a <κ-complete, non-principal ultrafilter over κ. Specifically, one may take the filter to be $\{A \vert A \subseteq \kappa \land \kappa \in j (A) \} \,.$ Generally, there will be many other <κ-complete, non-principal ultrafilters over κ. However, j might be different from the ultrapower(s) arising from such filter(s).