Conserving involution in residuated structures
Ai‐ni Hsieh, James Raftery · Mathematical logic quarterly · 2007
Abstract This paper establishes several algebraic embedding theorems, each of which asserts that a certain kind of residuated structure can be embedded into a richer one. In almost all cases, the original structure has a compatible involution, which must be preserved by the embedding. The results, in conjunction with previous findings, yieldseparativeaxiomatizations of thededucibility relationsof various substructural formal systems having double negation and contraposition axioms. The separation theorems go somewhat further than earlier ones in the literature, which either treated fewer subsignatures or focussed on the conservation of theorems only. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)