An introduction to C-minimal structures and their cell decomposition theorem
نویسنده
چکیده
Developments in valuation theory, especially the study of algebraically closed valued fields, have used the model theory of C-minimal structures in different places, e.g., the work of Hrushovski-Kazdhan in [HK06] and Haskell-Hrushovski-Macpherson in [HHM13]. We intend with this text both to promulgate a basic comprehension of Cminimality for mathematicians interested in valuation theory (equipped with a basic knowledge of model theory), and to provide a slightly different presentation of the cell decomposition theorem proved by Haskell and Macpherson in [HM94]. 2010 Mathematics Subject Classification. Primary 03C64; Secondary 13A18.
منابع مشابه
Introduction to O-minimal Structures and an Application to Neural Network Learning
1. Definition of o-minimality and first examples 1 2. Basic real analysis and the monotonicity theorem 4 3. Definable Skolem functions and elimination of imaginaries 8 4. Dimension, part 1 10 5. Cell decomposition 11 6. Dimension, part 2 15 7. Restricted analytic functions and global exponentiation 17 8. NIP and neural networks 20 8.1. Vapnik-Chervonenkis dimension 20 8.2. O-minimal structures ...
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