Towards a pseudoequational proof theory

ALMEIDA, Jorge and Ondřej KLÍMA. Towards a pseudoequational proof theory. Portugaliae mathematica. Lisboa, 2018, vol. 75, No 2, p. 79-119. ISSN 0032-5155. Available from: https://dx.doi.org/10.4171/PM/2012.

Basic information

• Original name: Towards a pseudoequational proof theory
• Authors: ALMEIDA, Jorge (620 Portugal) and Ondřej KLÍMA (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Portugaliae mathematica, Lisboa, 2018, 0032-5155.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Portugal
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.500
• RIV identification code: RIV/00216224:14310/18:00101744
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.4171/PM/2012
• UT WoS: 000452893900001
• Keywords in English: Pseudoidentity; syntactical proof; semigroup; profinite monoid; completeness; reducible pseudovariety; implicit signature
• Tags: International impact, Reviewed

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 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.

Links

• GA15-02862S, research and development project: Name: Aplikace algebry a kombinatoriky v teorii formálních jazyků

Investor: Czech Science Foundation