北京大学学报（自然科学版）

L(Q)格值模型的初等子模型

谢惠扬1,王捍贫2   

  1. 1北京林业大学基础科学与信息工程学院，北京，100083；2北京大学计算机科学与技术系，北京，100871
  • 收稿日期:2000-08-30 出版日期:2001-09-20 发布日期:2001-09-20

On Elementary Submodels of A Lattice-valued Model for Language L(Q)

XIE Huiyang1, WANG Hanpin2   

  1. 1College of Fundamental Science & Technology, Beijing Forestry University, Beijing, 100083; 2Department of Computer Science & Technology, Peking University, Beijing 100871
  • Received:2000-08-30 Online:2001-09-20 Published:2001-09-20

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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

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

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