Archive for Mathematical Logic 29 (4):213-229 (1990)

Abstract
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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DOI 10.1007/BF01651325
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References found in this work BETA

Second-Order Quantifiers and the Complexity of Theories.J. T. Baldwin & S. Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (3):229-303.
Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Coinductive ℵ0-Categorical Theories.James H. Schmerl - 1990 - Journal of Symbolic Logic 55 (3):1130 - 1137.
Complete Theories with Only Universal and Existential Axioms.A. H. Lachlan - 1987 - Journal of Symbolic Logic 52 (3):698-711.
Coinductive $Aleph_0$-Categorical Theories.James H. Schmerl - 1990 - Journal of Symbolic Logic 55 (3):1130-1137.

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Citations of this work BETA

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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