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We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of a successor relation on the vertices of the graph is allowed, as long as the validity of formulas is independent on the choice of a particular successor.We show that when the degree is bounded, successor-invariant first-order logic is no more expressive than first-order logic.

Successor-Invariant First-Order Logic on Classes of Bounded Degree (Extended Abstract)