V2EX model theory

Model Theory

Definition / 释义

模型论:数理逻辑的一个分支,研究形式语言中的理论(公理与公式)与其在具体数学对象中对应的模型(结构)之间的关系,例如“某些语句在某个结构中是否为真”、不同结构是否满足同一组公理等。(也可泛指“用模型进行理论分析”的方法,但最常见含义是数理逻辑中的模型论。)

Pronunciation / 发音

/md()l θiri/ (US)
/md()l θiri/ (UK)

Examples / 例句

Model theory studies which structures satisfy a given set of axioms.
模型论研究哪些结构满足一组给定的公理。

Using model theory, researchers compared different models of arithmetic to understand what can and cannot be proven from certain assumptions.
借助模型论,研究者比较不同的算术模型,以理解在某些假设下哪些结论可以或不可以被证明。

Etymology / 词源

model 来自拉丁语 modulus(“尺度、范式”),在数学与逻辑中引申为“使一组公式为真的结构/解释”;theory 来自希腊语 theōria(“观察、思考”),后引申为“系统性的学说”。“model theory”作为术语在20世纪数理逻辑发展中固定下来,用以指研究“理论模型”对应关系的学科。

Related Words / 相关词

Literary Works / 文学作品

  • Model Theory C. C. Chang & H. J. Keisler(经典教材,系统奠基与发展)
  • Model Theory Wilfrid Hodges(影响广泛的综合性著作)
  • A Course in Model Theory David Marker(较易读的研究生入门教材)
  • Finite Model Theory Heinz-Dieter Ebbinghaus & Jrg Flum(有限模型方向的代表性著作)
  • Model Theory: An Introduction David Poizat(以较强直觉与风格化叙述著称的入门书)
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