In this innovative and largely self-contained textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, and numerous exercises of varying difficulty further consolidate the student's learning.
In this innovative and largely self-contained textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, and numerous exercises of varying difficulty further consolidate the student's learning.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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.
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