$\kappa$-complete

A structured set $S$ (typically a filter or a Boolean algebra) is $\kappa$-complete if, given any $K\subseteq S$ with , $\bigcap K\in S$. It is complete if it is $\kappa$-complete for all $\kappa$.

Similarly, a partial order is $\kappa$-complete if any sequence of fewer than $\kappa$ elements has an upper bound within the partial order.

A ${\mathrm{\aleph }}_1$-complete is called countably complete.