What does the automorphism group of a free abelian group A know about A?
| dc.creator | Tolstykh, Vladimir | |
| dc.date | 2007-01-25 | |
| dc.date.accessioned | 2026-07-07T07:43:03Z | |
| dc.date.available | 2026-07-07T07:43:03Z | |
| dc.description | 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. | |
| dc.description | A pre-publication preprint of a paper published in `2005 | |
| dc.identifier | https://arxiv.org/abs/math/0701752 | |
| dc.identifier | http://arxiv.org/abs/math/0701752 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122672 | |
| dc.subject | Logic | |
| dc.subject | Group Theory | |
| dc.subject | 03C60 (20F28, 20K30) | |
| dc.title | What does the automorphism group of a free abelian group A know about A? | |
| dc.type | text |