O-minimal Structures

(Abstract)

In the early 1980s, A. Pillay and C. Steinhorn introduced the notion of o-minimal structures, and explored some important properties of this well-behaved class of linearly ordered structures.

L.van den Dries also noticed that many propertities of semialgebraic sets and maps could be derived from a few simple axioms, essentially the axioms defining "o-minimal structures". In this talk, I will first introduce some elementary results of o-minimal structures, and provide characterizations of o-minimal ordered groups and rings. Then I will talk on some essential results in the subject of o-minimal structures.