Abstract: The two-value weak model for first order logic with generalized quantifier Q is generalized to be valued in complete weak complemented lattices. For finite linearly-ordered weak complemented lattice, some properties on elementary extension of models for L(Q), such as strong downward L-S-T Theorem and the preservation of the elementary diagram under elementary extensions, are discussed.

Key words: generalized quantifier, Lattice-valued Model, elementary submodel

摘要： 将带广义量词Q的一阶逻辑的二值弱模型推广到取值于完备弱可补格上。对有限的线性序弱可补格，讨论了关于 L(Q)模型的初等子模型的一些性质，如强升和强降L-S-T定理，初等图像在初等扩充下的保持性等。

关键词: 广义量词, 格值模型论, 初等扩充