September 2003 Finite conformal hypergraph covers and Gaifman cliques in finite structures
Ian Hodkinson, Martin Otto
Bull. Symbolic Logic 9(3): 387-405 (September 2003). DOI: 10.2178/bsl/1058448678


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.


Download Citation

Ian Hodkinson. Martin Otto. "Finite conformal hypergraph covers and Gaifman cliques in finite structures." Bull. Symbolic Logic 9 (3) 387 - 405, September 2003.


Published: September 2003
First available in Project Euclid: 17 July 2003

zbMATH: 1058.03031
MathSciNet: MR2005955
Digital Object Identifier: 10.2178/bsl/1058448678

Primary: 03C13
Secondary: 03B45 , 03B70 , 05C65 , 05C69

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

Rights: Copyright © 2003 Association for Symbolic Logic


This article is only available to subscribers.
It is not available for individual sale.

Vol.9 • No. 3 • September 2003
Back to Top