The disjunctivities of ω-languages Original Research Article

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. In this paper, we consider a congruence IL on X∗ and a congruence OL on Xω introduced by an ω-language L, called the infinitary syntactic congruence and the ω-syntactic congruence of L, respectively. If IL is the equality, then L is called an I-disjunctive ω-language. Some results concerning I-disjunctive ω-languages are obtained. If OL is the equality, then L is called an O-disjunctive ω-language. A construction of O-disjunctive ω-languages is given. Properties concerning O-disjunctive ω-languages are investigated. An ω-language such that every ω-dense subset of it is an O-disjunctive ω-language is called a completely O-disjunctive ω-language. A completely O-disjunctive ω-language is given. Properties concerning completely O-disjunctive ω-languages are studied in this note.