Basic Model Theory
简介：
模型理论一方面研究数学结构 (“模型”) 与形式语言 (可以在其中表达有关这些结构的陈述) 之间的关系。示例结构是: 具有通常算术运算的自然数，从代数，有序集等熟悉的结构。重点是一阶语言，其模型理论是最著名的。一个示例结果是Lowenheim定理 (该领域中最古老的定理): 某些不可数结构的一阶句子true也必须在某些可数结构中成立。还处理了二阶语言及其几个片段。正如标题所示，本书向读者介绍了模型理论的基本内容。一个特殊的功能是它使用了Ehrenfeucht游戏，使读者熟悉模型世界。
英文简介：
Model theory investigates the relationships between mathematical structures ('models') on the one hand and formal languages (in which statements about these structures can be formulated) on the other. Example structures are: the natural numbers with the usual arithmetical operations, the structures familiar from algebra, ordered sets, etc. The emphasis is on first-order languages, the model theory of which is best known.
An example result is Lowenheim's theorem (the oldest in the field): a first-order sentence true of some uncountable structure must hold in some countable structure as well. Second-order languages and several of their fragments are dealt with as well.
As the title indicates, this book introduces the reader to what is basic in model theory. A special feature is its use of the Ehrenfeucht game by which the reader is familiarised with the world of models.
- 书名
- Basic Model Theory
- 译名
- 基本模型理论
- 语言
- 英语
- 年份
- 1996
- 页数
- 141页
- 大小
- 2.86 MB
- 下载
Basic Model Theory.pdf- 密码
- 65536
最后更新：2025-04-12 23:57:46