Submission date: 7 April 2020

Abstract:

Let O be the ring of integers of a number field, and let n ≥ 3. This paper studies bi-interpretability of the ring of integers ℤ with the special linear group SL_n(O), the general linear group GL_n(O) and solvable group of all invertible uppertriangular matrices over O, T_n(O). For each of these groups we provide a complete characterization of arbitrary models of their complete elementary theories.

Mathematics Subject Classification: 03C60, 20F16

Keywords and phrases:

Full text arXiv 2004.03585: pdf, ps.