Overconvergent real closed quantifier elimination

被引：10

作者：

Lipshitz, L.

Robinson, Z.

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] E Carolina Univ, Dept Math, Greenville, NC 27858 USA

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2006年 / 38卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1112/S0024609306018832

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be the (real closed) field of Puiseux series in t over R endowed with the natural linear order. Then the elements of the formal power series rings R[xi(1),...,xi(n)] converge t-adically on [-t, t](n), and hence define functions [-t, t](n) -> K. Let L be the language of ordered fields, enriched with symbols for these functions. By Corollary 3.15, K is o-minimal in L. This result is obtained from a quantifier elimination theorem. The proofs use methods from non-Archimedean analysis.

引用

页码：897 / 906

页数：10

共 8 条

[1] An effective version of Wilkie's theorem of the complement and some effective o-minimality results [J].

Berarducci, A ;

Servi, T .

ANNALS OF PURE AND APPLIED LOGIC, 2004, 125 (1-3) :43-74

[2]

Bosch S., 1984, Non-Archimedean analysis

[3]

CLUCKERS R, IN PRESS ANN SCI ECO

[4] P-ADIC AND REAL SUBANALYTIC SETS [J].

DENEF, J ;

VANDENDRIES, L .

ANNALS OF MATHEMATICS, 1988, 128 (01) :79-138

[5]

Fresnel J., 2004, PROGR MATH, V218

[6]

HRUSHOVSKI E, IN PRESS J SYMBOLIC

[7]

SCHOUTENS H, 1994, COMPOS MATH, V94, P269

[8]

VANDENDRIES L, 1996, LOGIC FDN APPL, P137

← 1 →