Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets
- 12 March 1981
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 46 (1) , 101-120
- https://doi.org/10.2307/2273263
Abstract
Every ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-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 ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.Keywords
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