Towards a pseudoequational proof theory
Jorge Almeida, Ondřej Klíma · Portugaliae Mathematica · 2018
A new scheme for proving pseudoidentities from a given set \Sigma of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when \Sigma defines a locally finite variety, a pseudovariety of groups, more generally, of completely simple semigroups, or of commutative monoids. Many further examples for which the scheme is complete are given when \Sigma defines a pseudovariety V which is \sigma -reducible for the equation x = y , provided \Sigma is enough to prove a basis of identities for the variety of \sigma -algebras generated by V. This gives ample evidence in support of the conjecture that the proof scheme is complete in general.