Roman Kossak

Mathematical Logic (eBook, PDF)

On Numbers, Sets, Structures, and Symmetry

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 257
• Erscheinungstermin: 18. April 2024
• Englisch
• ISBN-13: 9783031562150
• Artikelnr.: 70400262

Autorenporträt

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 38 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.

Inhaltsangabe

Part I: Logic, Sets, and Numbers.- Chapter 1. First-order Logic.- Chapter 2. Logical seeing.- Chapter 3. What is a Number?.- Chapter 4. Seeing the Number Structures.- Chapter 5. Points, Lines, and the Structure of R.- Chapter 6. Set Theory.- Part II: Relations, Structures, Geometry.- Chapter 7. Relations.- Chapter 8. Definable Elements and Constants.- Chapter 9. Minimal and Order-Minimal Structures.- Chapter 10. Geometry of Definable Sets.- Chapter 11. Where Do Structures Come From?.- Chapter 12. Elementary Extensions and Symmetries.- Chapter 13. Tame vs. Wild.- Chapter 14. First-Order Properties.- Chapter 15. Symmetries and Logical Visibility One More Time.- Part III: Inference, Models, Categoricity and Diversity.- Chapter 16. Logical Inference.- Chapter 17. Categoricity.- Chapter 18. Counting Countable Models.- Chapter 19. Infinitary Logics.- Chapter 20. Symmetry and Definability.- Appendices.- Bibliography.- Index.

Rezensionen

"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)