We consider the variety Lang generated by all language structures (PΣ, ·, ⊗, +, 0, 1), and the variety Lg≤ of ordered algebras generated by the structures (PΣ, ·, ⊗, 0, 1, ⊆), where PΣ is the powerset of Σ*, and where B · C is the complex concatenation of the languages B, C ⊆ Σ*, B ⊗ C is their shuffle product, and B + C is their union. We prove that for each finite set E of equations valid in Lang there is a (finite) model SE of E in which some inequation valid in Lg≤ fails. It follows that neither variety is finitely axiomatizable.
ASJC Scopus subject areas
- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics