eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2010-01-01
Vol. 12 no. 1
Automata, Logic and Semantics
10.46298/dmtcs.510
510
journal article
Deciding whether the ordering is necessary in a Presburger formula
Christian Choffrut
Achille Frigeri
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.
https://dmtcs.episciences.org/510/pdf
Presburger arithmetics
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]