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

Authors: Benjamin Rossman

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}
  }