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  1. The structure of the models of decidable monadic theories of graphs.D. Seese - 1991 - Annals of Pure and Applied Logic 53 (2):169-195.
    In this article the structure of the models of decidable monadic theories of planar graphs is investigated. It is shown that if the monadic theory of a class K of planar graphs is decidable, then the tree-width in the sense of Robertson and Seymour of the elements of K is universally bounded and there is a class T of trees such that the monadic theory of K is interpretable in the monadic theory of T.
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  • Monadic theory of order and topology in ZFC.Yuri Gurevich & Saharon Shelah - 1982 - Annals of Mathematical Logic 23 (2-3):179-198.
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  • Simple monadic theories and partition width.Achim Blumensath - 2011 - Mathematical Logic Quarterly 57 (4):409-431.
    We study tree-like decompositions of models of a theory and a related complexity measure called partition width. We prove a dichotomy concerning partition width and definable pairing functions: either the partition width of models is bounded, or the theory admits definable pairing functions. Our proof rests on structure results concerning indiscernible sequences and finitely satisfiable types for theories without definable pairing functions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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