Towards a pseudoequational proof theory

  • Jorge Almeida

    Universidade do Porto, Portugal
  • Ondřej Klíma

    Masaryk University, Brno, Czechia

Abstract

A new scheme for proving pseudoidentities from a given set of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when 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 defines a pseudovariety V which is -reducible for the equation , provided is enough to prove a basis of identities for the variety of -algebras generated by V. This gives ample evidence in support of the conjecture that the proof scheme is complete in general.

Cite this article

Jorge Almeida, Ondřej Klíma, Towards a pseudoequational proof theory. Port. Math. 75 (2018), no. 2, pp. 79–119

DOI 10.4171/PM/2012