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 $O$ be the ring of integers of a number field, and let $n\geq 3 $. T h i s p a p e r s t u d i e s b i - i n t e r p r e t a b i l i t y o f t h e r i n g o f i n t e g e r s$ $Z$ $w i t h t h e s p e c i a l l i n e a r g r o u p$ $SL$ _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.

Bi-interpretability with $Z$ and models of the complete elementary theories of ${SL}_{n} (O)$ , $T_{n} (O)$ and ${GL}_{n} (O)$ , $n \geq 3$

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Bi-interpretability with $Z$ and models of the complete elementary theories of ${SL}_{n} (O)$ , $T_{n} (O)$ and ${GL}_{n} (O)$ , $n \geq 3$

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Bi-interpretability with ZZ and models of the complete elementary theories of SLn(O)SLn​(O), Tn(O)Tn​(O) and GLn(O)GLn​(O), n≥3n≥3

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Bi-interpretability with ZZ and models of the complete elementary theories of SLn(O)SLn​(O), Tn(O)Tn​(O) and GLn(O)GLn​(O), n≥3n≥3

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Bi-interpretability with $Z$ and models of the complete elementary theories of ${SL}_{n} (O)$ , $T_{n} (O)$ and ${GL}_{n} (O)$ , $n \geq 3$

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Bi-interpretability with $Z$ and models of the complete elementary theories of ${SL}_{n} (O)$ , $T_{n} (O)$ and ${GL}_{n} (O)$ , $n \geq 3$

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AI智能校验