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O-minimal expansions of the reals Ingram, Patrick Malte Josef

Abstract

We survey recent results on o-rninimal theories, and in particular o-minimal expansions of real closed fields. The recent work in the classification of reducts of the field of real numbers, largely the work of Peterzil, is presented, as is the basic groundwork of o-rriinimality. It is shown that if X ⊆ℝⁿ is semialgebraic, but not semilinear, then multiplication on ℝ may be defined locally in terms of X, modulo the vector space properties of the reals. If X \ K is not semilinear for any compact K, then the condition of locality can be removed.

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