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Successor-invariant first-order logic on finite structures

Published online by Cambridge University Press:  12 March 2014

Benjamin Rossman
Benjamin Rossman*
Affiliation:
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, E-mail: brossman@theory.csail.mit.edu
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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
The Journal of Symbolic Logic , Volume 72 , Issue 2 , June 2007 , pp. 601 - 618
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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