Studia Logica 71 (1):31-46 (2002)

Abstract
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 (L 0) 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.
Keywords Lambek Calculus  cut rule  axiomatizability
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Reprint years 2004
DOI 10.1023/A:1016382907414
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On the Directional Lambek Calculus.Wojciech Zielonka - 2010 - Logic Journal of the IGPL 18 (3):403-421.

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