Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-interpretability with $\mathbb{Z}$ and models of the complete
  elementary theories of $\text{SL}_n(\mathcal{O})$, $\text{T}_n(\mathcal{O})$
  and $\text{GL}_n(\mathcal{O})$, $n\geq 3$   Let $\mathcal{O}$ be the ring of integers of a number field, and let $n\geq
3$. This paper studies bi-interpretability of the ring of integers $\mathbb{Z}$
with the special linear group $\text{SL}_n(\mathcal{O})$, the general linear
group $\text{GL}_n(\mathcal{O})$ and solvable group of all invertible
uppertriangular matrices over $\mathcal{O}$, $\text{T}_n(\mathcal{O})$. For
each of these groups we provide a complete characterization of arbitrary models
of their complete elementary theories.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex