Towards a pseudoequational proof theory
Group Theory
2019-03-18 v1
Abstract
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 when 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.
Keywords
Cite
@article{arxiv.1708.09681,
title = {Towards a pseudoequational proof theory},
author = {Jorge Almeida and Ondřej Klíma},
journal= {arXiv preprint arXiv:1708.09681},
year = {2019}
}