Bi-interpretability with ℤ and models of the complete elementary theories of SL_n(O), T_n(O) and GL_n(O), n≥ 3

2020/04/07 by Sohrabi, Mahmood, Myasnikov, Alexei G.
#03C60 #20F16 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2004.03585

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.

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