格蕴涵代数的模型论性质

On Model Properties of Lattice Implication Algebra

讨论有关格蕴涵代数结构的模型论性质 ,证明了形式化格蕴涵代数理论T保子模型、保模型链之并、保模型同态 ,理论T不是完备的、也不是模型完备的 ,因而不存在内在Skolem函数。另外 ,文中借助于超滤概念提出了格蕴涵代数簇的超积及格蕴涵代数中模糊子集的模糊超积 ,并进而研究了模糊滤子、模糊关联滤子及模糊子格蕴涵代数的相应性质。

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 theory T , it is proved that T is preserved under submodels, unions of chains and homomorphisms; T is 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.