THERE ARE NO INTERMEDIATE STRUCTURES BETWEEN THE GROUP OF INTEGERS AND PRESBURGER ARITHMETIC
THERE ARE NO INTERMEDIATE STRUCTURES BETWEEN THE GROUP OF INTEGERS AND PRESBURGER ARITHMETIC
Abstract We show that if a first-order structure ${\cal M}$ , with universe ℤ, is an expansion of (ℤ,+,0) and a reduct of (ℤ,+,<,0), then ${\cal M}$ must be interdefinable with (ℤ ,+,0) or (ℤ ,+,<,0).