Extensions of S1S and the Composition Method 1 Introduction - Irisa

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on infinite words [1]) and the model-theoretic one (Shelah's composition method [5, 16]). A ... and Thomas' class of profinitely ultimately periodic predicates, which includes unary ..... b, for some i ∈ I, or a ∈ Ai,b ∈ Aj, and i < j, and ∪i∈IP :=.
Extensions of S1S and the Composition Method Giovanna D’Agostino, Angelo Montanari, and Alberto Policriti Dipartimento di Matematica e Informatica, Universit`a di Udine via delle Scienze 206, 33100 Udine, Italy {dagostin|montana|policriti}@dimi.uniud.it

Abstract The study of the decidability of the monadic second-order (MSO) theory of (ω,