Diophantine geometry over groups III: Rigid and solid solutions

Z. Sela

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Diophantine geometry over groups III: Rigid and solid solutions

机译：III组上的丢番图几何：刚性和固溶体

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This paper is the third in a series 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 third paper we analyze exceptional families of solutions to a parametric system of equations. The structure of the exceptional solutions, and the global bound on the number of families of exceptional solutions we obtain, play an essential role in our approach towards quantifier elimination in the elementary theory of a free group presented in the next papers of this series. The argument used for proving the global bound is a key in proving the termination of the quantifier elimination procedure presented in the sixth paper of the series.

机译：本文是有关自由组中方程组的解的集的结构，此类集的投影以及在自由组上定义的基本集的结构的系列文章中的第三篇。在第三篇论文中，我们分析了参数方程组的特殊解系列。例外解决方案的结构以及我们所获得的例外解决方案族的数量的全局界限，在本系列下一篇文章中介绍的自由群基本理论中，在消除量词的方法中起着至关重要的作用。用于证明全局界限的论点是证明该系列第六篇论文中提出的量词消除程序终止的关键。

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《Israel Journal of Mathematics》 |2005年第1期|1-73|共73页
作者
Z. Sela;
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Institute of Mathematics The Hebrew University of Jerusalem;

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Diophantine geometry over groups III: Rigid and solid solutions

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