The monadic second-order logic of graphs. IV: Definability properties of equational graphs.

*(English)*Zbl 0731.03006This 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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\textit{B. Courcelle}, Ann. Pure Appl. Logic 49, No. 3, 193--255 (1990; Zbl 0731.03006)

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