  We characterise the Priestley spaces corresponding to affine complete bounded
distributive lattices. Moreover we prove that the class of affine complete
bounded distributive lattices is closed under products and free products. We
show that every (not necessarily bounded) distributive lattice can be embedded
in an affine complete one and that $\mathbb{Q} \cap [0,1]$ is initial in the
class of affine complete lattices.

Logic