Deciding whether the ordering is necessary in a Presburger formula
Christian Choffrut, Achille Frigeri · Discrete Mathematics & Theoretical Computer Science · 2010
Automata, Logic and Semantics 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.