关于无限值格模型论的一点注记

A NOTE ON LATTICE-VALUED MODEL THEORY

在[2],[3]中证明了当值格 L 有限时,紧致性定理成立.当值格 L 无限时紧性定理是否成立呢?说的更明确一点就是:设 T 是一个理论（分组句子集）且 T 的每一有限子集有模型（T 是有限和谐的）,T 有没有模型呢?我们的结论是:在一般情况下 T 不一定有模型.例1.设 L 是一可数无限格,L 含有一个如下的元素列:I>α1>α2>……>αn>……且 inf{αi}=0……

This paper contains two parts. In part Ⅰ,we give some counter-examples to illustrate that the compact- hess theorem in lattice-valued model theory no more holds generally when the value lattice is infinite. In partⅡ,we give an analogue of Makkai′s,definition of ‘consistency property’and the corresponding Model Existence Theorem for the case of lattice-valued model theory of finite language.