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

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

2007-01-25

arxiv.org/abs/math/0701752v1

Mathematics

Logic

A pre-publication preprint of a paper published in `2005

Scientific paper

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 $|A|$ 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 $|A_1|,|A_2|$ are second-order equivalent.

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