What does the automorphism group of a free abelian group A know about A?

被引：0

作者：

Tolstykh, V ^{[1
]}

机构：

[1] Yeditepe Univ, Dept Math, TR-34755 Istanbul, Turkey

来源：

Logic and Its Applications | 2005年 / 380卷

关键词：

automorphism groups; free algebras; free abelian groups; interpretations; first-order theories; high-order theories;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be an infinitely generated free abelian group. We prove that the automorphism group Aut(A) first-order interprets the full second-order theory of the set vertical bar A vertical bar with no structure. In particular, this implies that the automorphism groups of two infinitely generated free abelian groups A(1), A(2) are elementarily equivalent if and only if the sets vertical bar A(1)vertical bar, vertical bar A(2)vertical bar are second-order equivalent.

引用

页码：283 / 296

页数：14

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