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The monadic second-order logic of graphs. IV: Definability properties of equational graphs. (English) Zbl 0731.03006
This paper continues the author’s study of the monadic second-order logic of countable graphs [see Inf. Comput. 85, No.1, 12-75 (1990; Zbl 0722.03008); Math. Syst. Theory 21, No.4, 187-221 (1989; Zbl 0694.68043)]. It is shown that every equational graph can be characterized, up to isomorphism, by a formula of monadic second-order logic. It follows that the isomorphism of two equational graphs is decidable. The author also establishes that a graph specified in an equational graph by monadic second-order formulas is equational.
Reviewer: Li Xiang (Guiyang)

MSC:
03B25 Decidability of theories and sets of sentences
68R10 Graph theory (including graph drawing) in computer science
03C85 Second- and higher-order model theory
03B15 Higher-order logic; type theory (MSC2010)
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