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o-minimal structures on the field of real numbers. (English) Zbl 0854.03036
This is a survey of recent work on \(o\)-minimality. Many results are discussed, but none proved. No background in model theory is needed to read the paper. The notion of \(o\)-minimality is defined only for the reals, and an \(o\)-minimal structure on the field of real numbers is presented as a family of sets of \(n\)-tuples (for all \(n)\) with additional properties. There is a discussion of consequences of \(o\)-minimality (for example the Monotonicity, Cell Decomposition, and Triangulation Theorems), a description of some classes of \(o\)-minimal structures and Miller’s exponential growth rate dichotomy theorem, and some comments on applications.

MSC:
03C52 Properties of classes of models
12L12 Model theory of fields
12D99 Real and complex fields
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
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