Categoricity theory for lattice-valued model theory

A proof is presented of a version of the Morley categoricity theorem in lattice-valued model theory. Some useful notions, such as stable theory, indiscernible set, etc., are introduced into the lattice-valued model theory. The strong downward L-S-T theorem is proved to be true for the infinite value lattice L, although the compactness theorem does not hold in that case