For any set $X$ we denote by $\text{Part}(X)$ the set of all partitions of $X$, ordered by the refinement ordering. It is well known that this is a complete lattice for all sets $X$.


Let $L$ be a finite lattice. Is there a finite set such that there is an injective lattice homomorphism $\varphi:L\to\text{Part}(S)$ for some finite set $S$?



Embedding finite lattices into the lattice of partitions of a finite set
Yes, this is apparently a fairly hard theorem of [Pudlak and Tuma](http://link.springer.com/article/10.1007%2FBF02482893) (or at least I assume it is hard, because it seems to have been an open problem for decades before they finally proved it in 1980).


