论文标题
真实价值结构的模型理论
Model Theory for Real-valued Structures
论文作者
论文摘要
我们考虑公式在实际单位间隔中具有真实价值的通用结构，如在连续模型理论中，但相对于距离谓词，其谓词和功能并不一定是连续的。每个通用结构都可以通过添加一个均匀的公式极限来扩展到预先实现的结构。此外，该距离谓词是独特的，直到均匀的等效性。我们使用它将公制结构模型理论中的中心概念扩展到一般结构，并表明许多关于公制结构的文献的模型理论结果具有对通用结构的自然类似物。
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly continuous with respect to a distance predicate. Every general structure can be expanded to a pre-metric structure by adding a distance predicate that is a uniform limit of formulas. Moreover, that distance predicate is unique up to uniform equivalence. We use this to extend the central notions in the model theory of metric structures to general structures, and show that many model-theoretic results from the literature about metric structures have natural analogues for general structures.
