o-Minimal Structures
Lou van den Dries · 1996
Abstract The theory of o-minimal structures is a creation of model theorists, but is also intimately connected to “tame topology”. By tame topology I refer to the emerging idea that spaces of “finite type” deserve special attention: these spaces have aspects that tend to be overlooked when treated only within the general framework of (differential) topology. On the other hand, these aspects become prominent when we view these spaces as definable in model-theoretically “nice” structures. Thus the theory of o-minimal structures realizes to a large extent Grothendieck’s program of ‘topologie moderee’ outlined on pp. 25-42 of the fascinating document [Grothendieck, 1984). In some ways it also goes beyond this program.