van den Dries, Lou o-minimal structures on the field of real numbers. (English) Zbl 0854.03036 Jahresber. Dtsch. Math.-Ver. 98, No. 3, 165-171 (1996). 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. Reviewer: H.D.Macpherson (Leeds) Cited in 1 Document 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 Keywords:semialgebraic; subanalytic; \(o\)-minimal structure; survey; field of real numbers × Cite Format Result Cite Review PDF