Publication details
Towards a pseudoequational proof theory
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | Portugaliae mathematica |
| MU Faculty or unit | |
| Citation | |
| web | http://dx.doi.org/10.4171/PM/2012 |
| Doi | http://dx.doi.org/10.4171/PM/2012 |
| Keywords | Pseudoidentity; syntactical proof; semigroup; profinite monoid; completeness; reducible pseudovariety; implicit signature |
| Description | 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. |
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