On Model Properties of Lattice Implication Algebra

Lattice implication algebra is a new algebraic structure to study the lattice valued logic system. This paper is devoted to the study of the model properties of lattice implication algebra. For formalized lattice implication algebra theoryT, it is proved thatTis preserved under submodels, unions of chains and homomorphisms;Tis neither complete nor model complete, and hence there exists no built-in Skolem function. Moreover, the ultraproduct lattice implication algebras and the fuzzy ultraproduct of fuzzy subsets of lattice implication algebras are proposed by using the concept of ultrafilters, with the corresponding properties of fuzzy filters, fuzzy associative filters and fuzzy lattice implication subalgebras being discussed.