Ultraproduct of first-order lattice-valued logic LF(X) based on finite lattice implication algebra

In recent years, model theory has had remarkable success in solving important problems. Its importance lies in the observation that mathematical objects can be cast as models for a language. Ultraproduct is a method of constructing a new model from a family of models, In this paper, we deal with a new form of ultraproduct model for first-order lattice-valued logic LF(X) whose truth-value field is a finite lattice implication algebra. At the same time, Expansion theorem, two forms of fundamental theorem of ultraproducts and consistent theorem are obtained. Finally, another application of ultraproduct to algebra is discussed.