What form of the axiom of choice is equivalent (in ZF) to the statement that every distributive lattice is isomorphic to a lattice of sets?



Distributive lattices and axiom of choice
[According to Wikipedia](https://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem) the prime ideal theorem for distributive lattices is equivalent to the Boolean prime ideal theorem. (Look in the "Further prime ideal theorems" section.)


