## § Almost universal class

• A universal class is one that contains all subsets as elements.
• A class is almost universal if every subset of $L$ is a a subset of some element of $L$. But note that $L$ does not need to have all subsets as elements.
• $L$ is almost universal if for any subset $A \subset L$ (where $A$ is a set), there is some $B \in L$ such that $A \subseteq B$, but $A$ in itself need not be in $L$.