The disjunctivities of ω-languages

Abstract

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. Consider congruences IL and Pω, L on X* and a congruence OL on Xω introduced by an ω-language L. IL, Pω, L, and OL are called the infinitary syntactic-congruence, the principal congruence and the ω-syntactic congruence of L, respectively. If IL (Pω, L, OL) is the equality then L is called an I-disjunctive (P-disjunctive, O-disjunctive, respectively) ω- language. Properties concerning such ω-languages are explored and relations between these ω-languages are also studied.