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An Isaac Newton Institute Workshop

Model Theory, Algebraic and Analytic Geometry

Overconvergent Real Closed Quantifier Elimination

14th July 2005

Authors: Leonard Lipshitz (Purdue University), Zachary Robinson (East Carolina University)

Abstract

Let K be the (real closed) field of Puiseux series in t over the reals, R, endowed with the natural linear order. Then the elements of the formal power series rings R[[x_1,...,x_n]] converge t-adically on [-t,t]^n, and hence define functions [-t,t]^n to K. Let L be the language of ordered fields, enriched with symbols for these functions. We show that K is o-minimal in L. This result is obtained from a quantifier elimination theorem. The proofs use methods from non-Archimedean analysis.

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