Lics

IEEE Symposium on Logic in Computer Science

Paper: Successor-Invariance in the Finite (at LICS 2003)

Abstract

A first-order sentence \theta of vocabulary \sigma \cup {S} is successor-invariant in the finite if for every finite \sigma-structure M and successor relations S and S on M, (M,S) \models \theta \iff (M, S) \models \theta. 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.

BibTeX

 @InProceedings{Rossman-SuccessorInvariance,
 author = 	 {Benjamin Rossman},
 title = 	 {Successor-Invariance in the Finite},
 booktitle = {Proceedings of the Eighteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2003)},
 year =	 {2003},
 month =	 {June}, 
 pages = {148--157},
 location = {Ottawa, Canada}, 
 publisher =	 {IEEE Computer Society Press}
 }