دوره‌ای در نظریه مدل‌ها (یادداشت‌های درسی در منطق، شمارهٔ ۴۰)

This Concise Introduction To Model Theory Begins With Standard Notions And Takes The Reader Through To More Advanced Topics Such As Stability, Simplicity And Hrushovski Constructions. The Authors Introduce The Classic Results, As Well As More Recent Developments In This Vibrant Area Of Mathematical Logic. Concrete Mathematical Examples Are Included Throughout To Make The Concepts Easier To Follow. The Book Also Contains Over 200 Exercises, Many With Solutions, Making The Book A Useful Resource For Graduate Students As Well As Researchers. Ch. 1. The Basics -- Ch. 2. Elementary Extensions And Compactness -- Ch. 3. Quantifier Elimination -- Ch. 4. Countable Models -- Ch. 5. N1-categorial Theories -- Ch. 6. Morley Rank -- Ch. 7. Simple Theories -- Ch. 8. Stable Theories -- Ch. 9. Prime Extensions -- Ch. 10. The Fine Structure Of N1-categorical Theories. By Katrin Tent, Martin Ziegler. Includes Bibliographical References And Index. Preface 1. The basics 2. Elementary extensions and compactness 3. Quantifier elimination 4. Countable models 5. Aleph-1-categorical theories 6. Morley rank 7. Simple theories 8. Stable theories 9. Prime extensions 10. The fine structure of 1-categorical theories A. Set theory B. Fields C. Combinatorics D. Solutions of exercises Bibliography Index. This concise introduction takes the reader from standard notions to more advanced topics. It introduces the classic results, as well as more recent developments in this vibrant area of mathematical logic. Many worked examples and exercises make the book a useful resource for graduate students as well as researchers. Concise introduction to current topics in model theory, including simple and stable theories