Constructive negation has been proved to be a valid alternative to negation as failure, especially when negation is required to have, in a sense, an `active' role. In this paper we analyze an extension of the original constructive negation in order to gracefully integrate with the management of set-constraints in the context of a Constraint Logic Programming Language dealing with finite sets. We show that the marriage between CLP with sets and constructive negation gives us the possibility of representing a general class of intensionally defined sets without any further extension to the operational semantics of the language. The presence of intensional sets allows a definite in the expressive power and abstraction level offered by the host logic language.