This book grew out of a Survey Lecture given to the Association for Symbolic Logic meeting in January 1969 and is based on a course at the University of Wisconsin in the spring of 1969. It is planned both as a textbook for an advanced graduate course and as a reference for research work in mathematical logic.
We have written for the reader who already has a thorough knowledge of ‘classical’ model theory, that is, model theory for the usual first order predicate logic. The necessary background is given in the book MODEL THEORY by C. C. Chang and H. J. Keisler.
Author(s): H. Jerome Keisler
Series: Studies in logic and the foundations of mathematics 62
Publisher: North-Holland Publishing
Year: 1971
Language: English
Pages: 204
City: Amsterdam ; London
Preface......Page 4
Contents......Page 6
1. Introduction......Page 8
2. Scott's Isomorphism Theorem......Page 12
3. Model Existence Theorem......Page 15
4. Completeness Theorem......Page 20
5. Craig Interpolation Theorem......Page 24
6. Lyndon Interpolation Theorem......Page 29
7. Malitz Interpoloation Theorem......Page 34
8. Admissable Sets......Page 39
9. Barwise Compactness Theorem......Page 47
10. Undefinability of Well-order......Page 54
11. Omitting Types Theorem......Page 59
12. Prime Models......Page 66
13. Skolem Functions and Indiscernables......Page 70
14. Erdos-Rado Theorem......Page 78
15. The Hanf Number of L_{ω_1,ω}......Page 81
16. The Hanf Number of L_A......Page 86
17. Morley's Two Cardinal Theorem......Page 91
18. Categoricity in Power......Page 94
19. Homogeneous Models......Page 98
20. End Elementary Extensions......Page 105
21. Elementary Chains......Page 109
22. Another Two Cardinal Theorem......Page 115
23. More about Categoricity in Power......Page 123
24. Extending Models of Set Theory......Page 132
25. Short, Uncountable Models of Set Theory......Page 138
26. Lebesgue Measure......Page 144
27. The Property of Baire......Page 151
28. Second Order Number Theory......Page 154
29. A Three Cardinal Theorem......Page 160
30. End Elementary Extensions which Omit a Type......Page 163
31. Models of Power ω_1......Page 168
32. Ultrapowers......Page 176
33. Ultrapowers of models of set theory......Page 182
34. The Seven Cardinal Theorem......Page 186
References......Page 190
Author Index......Page 201
Index of Definitions......Page 202
Index of Symbols......Page 204
