Mathematical logic : on numbers, sets, structures, and symmetry
Author(s)
Bibliographic Information
Mathematical logic : on numbers, sets, structures, and symmetry
(Springer graduate texts in philosophy, v. 3)
Springer, c2018
Available at 5 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. 183-184) and index
Description and Table of Contents
Description
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.
Table of Contents
Chapter1. Mathematical Logic.- Chapter2. Logical Seeing.- Chapter3. What is a Number?.- Chapter4. Number Structures.- Chapter5. Points, Lines.- Chapter6. Set Theory.- Chapter7. Relations.- Chapter8. Definable Elements and Constants.- Chapter9. Minimal and Order-Minimal Structures.- Chapter10. Geometry of Definable Sets.- Chapter11. Where Do Structures Come From?.- Chapter12. Elementary Extensions and Symmetries.- Chapter13. Tame vs. Wild.- Chapter14. First-order Properties.- Chapter15. Symmetries and Logical Visibility One More Time.
by "Nielsen BookData"