Are all set lattices isomorphic to a power set? A set lattice is a lattice where the meet is the intersection, the join is the union, and the partial order is $\subseteq$. The standard example is is $P(A)$ where $A$ is a set. I’ve thought about other possible examples, yet have failed to come up with any. Are there any set/distributive lattices that aren’t isomorphic to $P(A)$ for some $A$?

Total orders with $\land = \min$ and $\lor = \max$ are lattices and any of them, call it $(X,\le)$ and call $(-\infty,x)=\{y\in X\,:\, y<x\}$, is isomorphic to the set lattice $(\{(-\infty,x)\,:\, x\in X\}, \subseteq)$. However, $P(A)$ is hardly ever totally ordered.
