Model Theory For Infinitary Logic (eBook)

Front Cover 1
Model Theory for Imfinitary Logic 4
Copyright Page 5
Table of Contents 10
PART I 12
Chapter 1. Introduction 14
Chapter 2. Scott’s Isomorphism Theorem 18
Chapter 3. Model Existence Theorem 21
Chapter 4. Completeness Theorem 26
Chapter 5. Craig Interpolation Theorem 30
Chapter 6. Lyndon Interpolation Theorem 35
Chapter 7. Malitz Interpolation Theorem 40
Chapter 8. Admissible sets 45
Chapter 9. Barwise Compactness Theorem 53
Chapter 10. Undefinability of well order 60
Chapter 11. Omitting Types Theorem 65
Chapter 12. Prime models 72
PART II 76
Chapter 13. Skolem functions and indiscernibles 78
Chapter 14. Erdös-Rado Theorem 86
Chapter 15. The Hanf number of L.1. 89
Chapter 16. The Hanf number of LA 94
Chapter 17. Morley’s Two Cardinal Theorem 99
Chapter 18. Categoricity in power 102
Chapter 19. Homogeneous models 106
Chapter 20. End elementary extensions 113
PART III 118
Chapter 21. Elementary chains 120
Chapter 22. Another two cardinal theorem 126
Chapter 23. More about categoricity in power 134
Chapter 24. Extending models of set theory 143
Chapter 25. Short, uncountable models of set theory 149
Chapter 26. Lebesgue measure 155
Chapter 27. The property of Baire 162
Chapter 28. Second order number theory 165
Chapter 29. A three cardinal theorem 171
Chapter 30. End elementary extensions which omit a type 174
Chapter 31. Models of power .1 179
PART IV 188
Chapter 32. Ultrapowers 190
Chapter 33. Ultrapowers of models of set theory 196
Chapter 34. The Seven Cardinal Theorem 200
REFERENCES 204
AUTHOR INDEX 216
INDEX OF DEFINITIONS 217
INDEX OF SYMBOLS 219