On Ultrafilters of Lattice Implication Algebras

In model theories, constructing ultraproducts by ultrafilter is an important method for model construction. In this paper, the concept of ultrafilter of lattice implication algebras is proposed. The relationship between ultrafilters and prime filters, and the one between ultrafilters and finite intersection properties are discussed. The equivalence between ultrafilter and maximal proper filter is proved. It provides a foundation for studying the corresponding ultraproduct theory.