Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures,  show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications ansrs 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. AMS 2000 classification: primary 03C13, secondary 03B45, 03B70, 05C65, 05C69.
['Ian M. Hodkinson', 'Martin Otto']
I am writing a research paper on a idea Finite conformal hypergraph covers and Gaifman cliques in finite structures
[{"from": "human", "value": "I am writing a research paper on a idea Finite conformal hypergraph covers and Gaifman cliques in finite structures"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 \u2010 thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms,  show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures,  show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications ansrs 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. AMS 2000 classification: primary 03C13, secondary 03B45, 03B70, 05C65, 05C69."}]