Mathematical Logic

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

New edition includes countable categoricity, analyzed using examples from the first two parts of the book Presents an introduction to formal mathematical logic and set theory Presents simple yet nontrivial results in modern model theory

Auteur
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.

Contenu

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.

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