On reduction systems equivalent to the Lambek calculus with the empty string

The paper continues a series of results on cut-rule axiomatizability of the Lambek calculus. It provides a complete solution of a problem which was solved partially in one of the author's earlier papers. It is proved that the product-free Lambek Calculus with the empty string (L0) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut rule. The proof makes use of the (infinitely) cut-rule axiomatized calculus C designed by the author exactly for this purpose. © 2002 Kluwer Academic Publishers.