Geodesic
On elementary theories of integer linear groups
Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 919-934

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We study some restricted elementary theories of general, special and projective linear groups over the integers and discuss their algorithmic unsolvability. 
@article{IM2_1995_59_5_a2,
     author = {V. G. Durnev},
     title = {On elementary theories of integer linear groups},
     journal = {Izvestiya. Mathematics },
     pages = {919--934},
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     volume = {59},
     number = {5},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a2/}
}
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V. G. Durnev. On elementary theories of integer linear groups. Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 919-934. http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a2/