Let
Γ
\Gamma
be an infinite discrete subgroup of Gl
n
(
C
)
_n(\mathbb {C})
. Then either
(
R
,
>
,
+
,
⋅
,
Γ
)
(\mathbb {R},>,+,\cdot ,\Gamma )
is interdefinable with
(
R
,
>
,
+
,
⋅
,
λ
Z
)
(\mathbb {R},>,+,\cdot , \lambda ^{\mathbb {Z}})
for some real number
λ
\lambda
, or
(
R
,
>
,
+
,
⋅
,
Γ
)
(\mathbb {R},>,+,\cdot ,\Gamma )
defines the set of integers. When
Γ
\Gamma
is not virtually abelian, the second case holds.