Abstract
If \(\Gamma \) is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example \({{\,\mathrm{SL}\,}}_n({\mathbb {Z}})\), \(n \ge 3\)) and \(\Lambda \) is a finitely generated group that is elementarily equivalent to \(\Gamma \), then \(\Lambda \) is isomorphic to \(\Gamma \).
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Acknowledgements
The authors are grateful to Zlil Sela for fruitful conversations and insights which improved the original proof. We are also thankful to Goulnara Arzhantseva, Andre Nies, Andrei Rapinchuk and Tyakal Nanjundiah Venkataramana for pointing out to us several background references. Finally, we thank the anonymous referees for their careful reading and many suggestions. The first author was partially support by NSF Grant No. DMS-1303205 and BSF Grant No. 2012247. The second author was partially support by ERC, NSF and BSF. The third author was partially supported by ISF Grant No. 662/15 and BSF Grant No. 2014099.
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Avni, N., Lubotzky, A. & Meiri, C. First order rigidity of non-uniform higher rank arithmetic groups. Invent. math. 217, 219–240 (2019). https://doi.org/10.1007/s00222-019-00866-5
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DOI: https://doi.org/10.1007/s00222-019-00866-5