Article contents
Successor-invariant first-order logic on finite structures
Published online by Cambridge University Press: 12 March 2014
Abstract
We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (, S1) ⊨ Φ ⇔ (
, S2) ⊨ Φ for all finite structures
and successor relations S1, S2 on
. A successor-invariant sentence Φ has a well-defined semantics on finite structures
with no given successor relation: one simply evaluates Φ on (
, S) for an arbitrary choice of successor relation S. In this article, we prove that (FO + succ)inv is more expressive on finite structures than first-order logic without a successor relation. This extends similar results for order-invariant logic [8] and epsilon-invariant logic [10].
- Type
- Research Article
- Information
- Copyright
- Copyright © Association for Symbolic Logic 2007
References
REFERENCES
- 9
- Cited by