We consider language structures L∑ = (P∑, ·, ⊗, +, 1, 0), where P∑ consists of all subsets of the free monoid ∑*; the binary operations ·, ⊗ 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∑ 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∑, ·, ⊗, 1, ⊆), where ⊆ denotes set inclusion.
ASJC Scopus subject areas
- Information Systems
- Computer Networks and Communications