ON THE MODEL THEORY OF HIGHER RANK ARITHMETIC GROUPS

Nir Avni, Chen Meiri

Research output: Contribution to journalArticlepeer-review

Abstract

Let Г be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if Г is either nonuniform or is uniform of orthogonal type and dimension at least 9, then Г is bi-interpretable with the ring Z of integers. It follows that the first-order theory of Г is undecidable, that all finitely generated subgroups of Г are definable, and that Г is characterized by a single first-order sentence among all finitely generated groups.

Original languageEnglish (US)
Pages (from-to)2537-2589
Number of pages53
JournalDuke Mathematical Journal
Volume172
Issue number13
DOIs
StatePublished - 2023

ASJC Scopus subject areas

  • Mathematics(all)

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