Bulletin of Symbolic Logic

Finite conformal hypergraph covers and Gaifman cliques in finite structures

Ian Hodkinson and Martin Otto

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Abstract

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques—thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF.

Article information

Source
Bull. Symbolic Logic, Volume 09, Issue 3 (2003), 387- 405.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1058448678

Digital Object Identifier
doi:10.2178/bsl/1058448678

Mathematical Reviews number (MathSciNet)
MR2005955

Zentralblatt MATH identifier
1058.03031

Subjects
Primary: 03C13: Finite structures [See also 68Q15, 68Q19]
Secondary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45} 03B70: Logic in computer science [See also 68-XX] 05C65: Hypergraphs 05C69: Dominating sets, independent sets, cliques

Keywords
finite model theory extension property for partial isomorphisms guarded logics finite model property

Citation

Hodkinson, Ian; Otto, Martin. Finite conformal hypergraph covers and Gaifman cliques in finite structures. Bull. Symbolic Logic 09 (2003), no. 3, 387-- 405. doi:10.2178/bsl/1058448678. https://projecteuclid.org/euclid.bsl/1058448678


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