
Mathematical Logic
On Numbers, Sets, Structures, and Symmetry
Roman Kossak(Author)
Springer (Publisher)
1st Edition
Published on 18. October 2018
Book
Hardback
XIII, 186 pages
978-3-319-97297-8 (ISBN)
Article exhausted; check for reprint
Description
Presents an introduction to of formal mathematical logic and set theory
Presents simple yet nontrivial results in modern model theory
Provides introductory remarks to all results, including a historical background
Reviews / Votes
"Remembering how impenetrable textbooks on mathematical logic were when he was a freshman, the author has written an introductory textbook on mathematical logic, whose main strength is the emphasis on motivating every step with detailed explanations. . The author has clearly succeeded in writing a textbook making the reading of those impenetrable texts possible for a beginner." (Victor V. Pambuccian, zbMATH 06945597, 2021)"This fun book can be viewed as a very gentle introduction to the notion of mathematical structure, and hence to model theory. . Each chapter concludes with a selection of exercises of varying degrees of difficulty, often asking the reader to establish facts. Apart from the uses suggested on the book's cover, I can well imagine teaching an introduction to proof class with this textbook." (Jana Maríková, Mathematical Reviews, March 2021)
"The author has made a significant effort to present the (not so easy) material in an understandable way . . I am sure that readers of this well-written book will experience many such satisfying moments." (Temur Kutsia, Computing Reviews, September 11, 2019)
"Such modesty and humility. Wow. Here is an outstanding book. In the beginning, we learn of the difficulties the author encountered as a student while learning some of the very topics he writes about in this book. So successfully has the author conquered his youthful difficulties that model theory is now his research specialty and is also an important component of this book." (Dennis W. Gordon, MAA Reviews, May 19, 2019)
More details
Series
Edition
2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
College/higher education
Illustrations
28
28 s/w Abbildungen
XIII, 186 p. 28 illus.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
471 gr
ISBN-13
978-3-319-97297-8 (9783319972978)
DOI
10.1007/978-3-319-97298-5
Schweitzer Classification
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04/2024
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01/2019
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E-Book
10/2018
1st Edition
Springer
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Available for download
Person
Roman Kossak is a Professor of Mathematics at the City University of New York. He does research in model theory of formal arithmetic. He has published 36 research papers and co-authored a monograph on the subject for the Oxford Logic Guides series. His other interests include philosophy of mathematics, phenomenology of perception, and interactions between mathematics philosophy and the arts.
Content
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.