THERE ARE NO INTERMEDIATE STRUCTURES BETWEEN THE GROUP OF INTEGERS AND PRESBURGER ARITHMETIC
AbstractWe 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).
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1990 ◽
Vol 32
(2)
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pp. 180-192
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1963 ◽
Vol 3
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pp. 202-206
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1976 ◽
Vol 74
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pp. 91-113
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