Jonathan Kirby is a Senior Lecturer in Mathematics at the University of East Anglia. His main research is in model theory and its interactions with algebra, number theory, and analysis, with particular interest in exponential functions. He has taught model theory at the University of Oxford, the University of Illinois, Chicago, and the University of East Anglia.
Preface
Part I. Languages and Structures: 1. Structures
2. Terms
3. Formulas
4. Definable sets
5. Substructures and quantifiers
Part II. Theories and Compactness: 6. Theories and axioms
7. The complex and real fields
8. Compactness and new constants
9. Axiomatisable classes
10. Cardinality considerations
11. Constructing models from syntax
Part III. Changing Models: 12. Elementary substructures
13. Elementary extensions
14. Vector spaces and categoricity
15. Linear orders
16. The successor structure
Part IV. Characterising Definable Sets: 17. Quantifier elimination for DLO
18. Substructure completeness
19. Power sets and Boolean algebras
20. The algebras of definable sets
21. Real vector spaces and parameters
22. Semi-algebraic sets
Part V. Types: 23. Realising types
24. Omitting types
25. Countable categoricity
26. Large and small countable models
27. Saturated models
Part VI. Algebraically Closed Fields: 28. Fields and their extensions
29. Algebraic closures of fields
30. Categoricity and completeness
31. Definable sets and varieties
32. Hilbert's Nullstellensatz
Bibliography
Index.
