Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets

Journal of Symbolic Logic 46 (1):101 - 120 (1981)
Every ℵ 0 -categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ 0 -categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ 0 -categorical partially ordered set not embedding one of them has a decidable theory
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DOI 10.2307/2273263
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The Structure of the Models of Decidable Monadic Theories of Graphs.D. Seese - 1991 - Annals of Pure and Applied Logic 53 (2):169-195.

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