On some questions concerning the axiomatisation of WNM-algebras and their subvarieties (Q1697331)

The authors extend MTL-algebras by a one-variable axiom. They refer to its equivalent algebraic semantics as the variety of GHP-algebras, those algebras will be shown to form the largest variety of MTL-algebras such that the falsum-free reducts of the positive cones of their chains are the most general totally ordered Gödel hoops. Also, they obtain a general description of GHP standard algebras, and use the latter to characterise those extensions of WNM-algebras that can be obtained from GHP-algebras via the same set of extended axioms.