 Every distributive (∨,0)-semilattice is a direct limit of finite Boolean (∨,0)-semilattices and (∨,0)-homomorphisms.It should be observed that while the transition homomorphisms used in the Ershov-Pudlák Theorem are (∨,0)-embeddings, the transition homomorphisms used in the result above are not necessarily one-to-one, for example when one tries to represent the three-element chain.Practically this does not cause much trouble, and makes it possible to prove the following results.