F-Disjunctive languagest

A language L is f-disjunctive if every class of its syntactic congruence is finite. The family of f-disjunctive languages is a natural generalization of the family of disjunctive languages and both families are anti-AFL. Every f-disjunctive language is dense and every class (≠ 1) of its syntactic congruence is an infix code. Five different classes of f-disjunctive languages are considered and it is shown that they form a strict hierarchy. Also some properties of the syntactic monoid of a f-disjunctive language are established, in particular its decomposition as a subdirect product of nil monoids.