An Invitation to Model Theory
- Author: Jonathan Kirby, University of East Anglia
- Date Published: April 2019
- availability: Available
- format: Paperback
- isbn: 9781316615553
Paperback
-
Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative 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, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Read more- Suitable for use as an undergraduate- or Masters-level course in model theory, unlike traditional graduate-level texts
- Contains many exercises of varying difficulty, from bookwork to more substantial projects
- Presents model theory in the context of undergraduate mathematics via definable sets in familiar structures
Customer reviews
28th Jan 2019 by Niconi
I am looking forward to it and hope to take more in.
Review was not posted due to profanity
×Product details
- Date Published: April 2019
- format: Paperback
- isbn: 9781316615553
- length: 194 pages
- dimensions: 227 x 151 x 12 mm
- weight: 0.3kg
- contains: 5 b/w illus.
- availability: Available
Table of Contents
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.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×