Diophantine geometry over groups VI: The elementary theory of a free group

被引：119
|
作者：
Sela, Z. [1 ]
机构：
[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2006年 / 16卷 / 03期
关键词：
first order theory; Tarski problem; quantifier elimination; elementary equivalence; limit groups; omega-residually free towers;
D O I：
10.1007/s00039-006-0565-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the sixth paper we use the quantifier elimination procedure presented in the two parts of the fifth paper in the sequence, to answer some of A. Tarski's problems on the elementary theory of a free group, and to classify finitely generated (f.g.) groups that are elementarily equivalent to a non-abelian f.g. free group.
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页码：707 / 730
页数：24
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