Résumé: We consider language structures L('Sigma' ) = (P('Sigma' ),., x , +, 1, 0), where P('Sigma' ) consists of all subsets of the free monoid 'Sigma' (*); the binary operations., x and + are concatenation, shuffle product and union, respectively, and where the constant 0 is the empty set and the constant 1 is the singleton set containing the empty word. We show that the variety Lang generated by the structures L('Sigma' ) has no finite axiomatization. In fact we establish a stronger result: The variety Lang has no finite axiomatization over the variety of ordered algebras Lg(?) generated by the structures (P('Sigma' ),., x , I, 'inclus dans ou=' ), where 'inclus dans ou=' denotes set inclusion.

Langue: Anglais