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June 2007 Successor-invariant first-order logic on finite structures
Benjamin Rossman
J. Symbolic Logic 72(2): 601-618 (June 2007). DOI: 10.2178/jsl/1185803625

Abstract

We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (𝔞,S1) ⊨ Φ {⋔} (𝔞,S2) ⊨ Φ for all finite structures 𝔞 and successor relations S1,S2 on 𝔞. A successor-invariant sentence Φ has a well-defined semantics on finite structures 𝔞 with no given successor relation: one simply evaluates Φ on (𝔞,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].

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Benjamin Rossman. "Successor-invariant first-order logic on finite structures." J. Symbolic Logic 72 (2) 601 - 618, June 2007. https://doi.org/10.2178/jsl/1185803625

Information

Published: June 2007
First available in Project Euclid: 30 July 2007

zbMATH: 1121.03041
MathSciNet: MR2320292
Digital Object Identifier: 10.2178/jsl/1185803625

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 2 • June 2007
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