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OVERCONVERGENT REAL CLOSED QUANTIFIER ELIMINATION

Published online by Cambridge University Press:  19 December 2006

L. LIPSHITZ  and
Z. ROBINSON
L. LIPSHITZ
Affiliation:
Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, IN 47907-2067, USAlipshitz@math.purdue.edu
Z. ROBINSON
Affiliation:
Department of Mathematics, East Carolina University, Greenville, NC 27858-4353, USArobinsonz@mail.ecu.edu
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Abstract

Let $K$ be the (real closed) field of Puiseux series in $t$ over ${\mathbf R}$ endowed with the natural linear order. Then the elements of the formal power series rings ${\mathbf R}[\![\xi_1,\dots,\xi_n]\!]$ converge $t$-adically on $[-t,t]^n$, and hence define functions $[-t,t]^n\to K$. Let ${\mathcal L}$ be the language of ordered fields, enriched with symbols for these functions. By Corollary 3.15, $K$ is o-minimal in ${\mathcal L}$. This result is obtained from a quantifier elimination theorem. The proofs use methods from non-Archimedean analysis.

Keywords

03C6432P0532B0532B2003C10 (primary)03C9803C6014P15 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 897 - 906
Copyright
The London Mathematical Society 2006

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Footnotes

Supported in part by NSF grant DMS-0401175.