Towards a pseudoequational proof theory

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Almeida, J (Author) FCUP; Klima, O (Author) Other

Journal

Title: Portugaliae Mathematica

Vol. 75

Pages: 79-119

ISSN: 0032-5155

Publisher: European Mathematical Society Publishing House

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00Q-0K9

DOI: 10.4171/pm/2012

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41