Mathematical Logic: On Numbers, Sets, Structures, and Symmetry


Mathematical Logic: On Numbers, Sets, Structures, and Symmetry (Springer Graduate Texts in Philosophy)
By 作者: Roman Kossak
ISBN-10 书号: 3319972979
ISBN-13 书号: 9783319972978
Edition 版本: 1st ed. 2018
Release Finelybook 出版日期: 2018-10-04
Pages 页数: (186 )

The Book Description robot was collected from Amazon and arranged by Finelybook

This book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions.
Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments.
The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures.
The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
Part l. Logic, Sets, and Numbers
1. First-Order Logic
2. Logical Seeing
3. What is a Number?
4. Seeing the Number Structures
5. Points, Lines, and the Structure of
6. Set Theory Partll. Relations, Structures, Geometry
7. Relations
8. Definable Elements and Constants
9. Minimal and Order-Minimal Structures
10. Geometry of Definable Sets
11. Where Do Structures Come From?
12. Elementary Extensions and Symmetries
13. Tame vs. Wild
14. First-Order Properties
15. Symmetries and Logical Visibility One More Time
16. Suggestions for Further Reading


下载地址

Mathematical Logic On Numbers, Sets, Structures, and Symmetry 9783319972978.zip

下载地址 DOWNLOAD隐藏内容需1积分,请先!没有帐号? 注 册 一个!
觉得文章有用就打赏一下文章作者
未经允许不得转载:finelybook » Mathematical Logic: On Numbers, Sets, Structures, and Symmetry
分享到: 更多 (0)

评论 抢沙发

  • 昵称 (必填)
  • 邮箱 (必填)
  • 网址

觉得文章有用就打赏一下文章作者

支付宝扫一扫打赏

微信扫一扫打赏