Discrete Mathematics & Theoretical Computer Science, Vol 12, No 1 (2010)

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Deciding whether the ordering is necessary in a Presburger formula

Christian Choffrut, Achille Frigeri


We characterize the relations which are first-order definable in the model of the group of integers with the constant 1. This allows us to show that given a relation defined by a first-order formula in this model enriched with the usual ordering, it is recursively decidable whether or not it is first-order definable without the ordering.

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