The first papers on o-minimal structures appeared about a decade ago, see [5], [19], [14]. Since then the subject has grown into a wide ranging generalization of semialgebraic and subanalytic geometry and topology. (Basic references are, on semialgebraic topics, and [16], [12] and [2] on subanalytic sets.) Here I give only a brief overview of o-minimal structures. In particular I restrict myself to o-minimal structures on the field of real numbers, omitting any proofs for the results stated. A systematic and selfcontained treatment of the subject is given in the book; see also [7] for an extensive survey with many references, and [9] for a more geometric discussion in the language of manifolds.
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