Successor-invariance in the finite

B. Rossman
18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.  
A first-order sentence θ of vocabulary σ ∪ {S} is successor-invariant in the finite if for every finite σ-structure M and successor relations S 1 and S 2 on M, In this paper I give an example of a non-first-order definable class of finite structures which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for order-invariance in the finite, due to Y. Gurevich.
doi:10.1109/lics.2003.1210054 dblp:conf/lics/Rossman03 fatcat:ot6dmgsfcjbu5ktbayjgwe66yu