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A course in model theory
להגדלת הטקסט להקטנת הטקסט- ספר
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.
| כותר |
A course in model theory / by Katrin Tent, Martin Ziegler. |
|---|---|
| מוציא לאור |
Cambridge : Cambridge University Press |
| שנה |
2012 |
| הערות |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). Includes bibliographical references and index. English |
| הערת תוכן ותקציר |
Cover A Course in Model Theory LECTURE NOTES IN LOGIC Copyright CONTENTS PREFACE Chapter 1 THE BASICS 1.1. Structures 1.2. Language 1.3. Theories Chapter 2 ELEMENTARY EXTENSIONS AND COMPACTNESS 2.1. Elementary substructures 2.2. The Compactness Theorem 2.3. The Löwenheim-Skolem Theorem Chapter 3 QUANTIFIER ELIMINATION 3.1. Preservation theorems 3.2. Quantifier elimination 3.3. Examples Chapter 4 COUNTABLE MODELS 4.1. The omitting types theorem 4.2. The space of types 4.3. א0-categorical theories 4.4. The amalgamation method 4.5. Prime models Chapter 5 א1-CATEGORICAL THEORIES5.1. Indiscernibles 5.2. ω-stable theories 5.3. Prime extensions 5.4. Lachlan's Theorem 5.5. Vaughtian pairs 5.6. Algebraic formulas 5.7. Strongly minimal sets 5.8. The Baldwin-Lachlan Theorem Chapter 6 MORLEY RANK 6.1. Saturated models and the monster 6.2. Morley rank 6.3. Countable models of א1-categorical theories 6.4. Computation of Morley rank Chapter 7 SIMPLE THEORIES 7.1. Dividing and forking 7.2. Simplicity 7.3. The independence theorem 7.4. Lascar strong types 7.5. Example: pseudo-finite fields Chapter 8 STABLE THEORIES 8.1. Heirs and coheirs8.2. Stability 8.3. Definable types 8.4. Elimination of imaginaries and Teq 8.5. Properties of forking in stable theories 8.6. SU-rank and the stability spectrum Chapter 9 PRIME EXTENSIONS 9.1. Indiscernibles in stable theories 9.2. Totally transcendental theories 9.3. Countable stable theories Chapter 10 THE FINE STRUCTURE OF א1-CATEGORICAL THEORIES 10.1. Internal types 10.2. Analysable types 10.3. Locally modular strongly minimal sets 10.4. Hrushovski's examples Appendix A SET THEORY A.1. Sets and classes A.2. Ordinals A.3. Cardinals Appendix B FIELDS B.1. Ordered fieldsB.2. Differential fields B.3. Separable and regular field extensions B.4. Pseudo-finite fields and profinite groups Appendix C COMBINATORICS C.1. Pregeometries C.2. The Erdös-Makkai Theorem C.3. The Erdös-Rado Theorem Appendix D SOLUTIONS TO EXERCISES Chapter 1. The basics Chapter 2. Elementary extensions and compactness Chapter 3. Quantifier elimination Chapter 4. Countable models Chapter 5. א1-categorical theories Chapter 6. Morley rank Chapter 7. Simple theories Chapter 8. Stable theories Chapter 9. Prime extensions Chapter 10. The fine structure of א1-categorical theoriesAppendices REFERENCES INDEX |
| סדרה |
Lecture notes in logic 40 |
| היקף החומר |
1 online resource (x, 248 pages) : digital, PDF file(s). |
| שפה |
אנגלית |
| מספר מערכת |
997010707040005171 |
תצוגת MARC
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