Finite conformal hypergraph covers and Gaifman cliques in finite structures

Bulletin of Symbolic Logic 9 (3):387-405 (2003)
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
Keywords finite model theory   extension property for partial isomorphisms   guarded logics   finite model property
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DOI 10.2178/bsl/1058448678
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References found in this work BETA
On the Restraining Power of Guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
Tolerance Logic.Maarten Marx - 2001 - Journal of Logic, Language and Information 10 (3):353-374.

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Citations of this work BETA
Modal and Guarded Characterisation Theorems Over Finite Transition Systems.Martin Otto - 2004 - Annals of Pure and Applied Logic 130 (1-3):173-205.
Complexity of Monodic Guarded Fragments Over Linear and Real Time.Ian Hodkinson - 2006 - Annals of Pure and Applied Logic 138 (1):94-125.
Expressive Completeness Through Logically Tractable Models.Martin Otto - 2013 - Annals of Pure and Applied Logic 164 (12):1418-1453.

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