关于BCK代数的模型论性质

摘要

This paper is devoted to the study of the logical properties of BCK algebras.For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no builtin Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding propertics of fuzzy ideals discussed.