Some coinductive graphs

Archive for Mathematical Logic 29 (4):213-229 (1990)
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LetT be a universal theory of graphs such that Mod(T) is closed under disjoint unions. Letℳ T be a disjoint union ℳ i such that eachℳ i is a finite model ofT and every finite isomorphism type in Mod(T) is represented in{ℳ i ∶i<Ω3}. We investigate under what conditions onT, Th(ℳ T ) is a coinductive theory, where a theory is called coinductive if it can be axiomatizated by ∃∀-sentences. We also characterize coinductive graphs which have quantifier-free rank 1



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Triviality, NDOP and stable varieties.B. Hart, A. Pillay & S. Starchenko - 1993 - Annals of Pure and Applied Logic 62 (2):119-146.

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Complete theories with only universal and existential axioms.A. H. Lachlan - 1987 - Journal of Symbolic Logic 52 (3):698-711.

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