A note on Sugihara algebras
In [41 Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, .and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it . In [3] it is stated that this quasivariety is the variety...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 1992 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/132479 |
| Online Access: | https://hdl.handle.net/2445/132479 |
| Access Level: | Open access |
| Keyword: | Àlgebra Anells (Àlgebra) Algebra Rings (Algebra) |
| _version_ | 1878730386307022848 |
|---|---|
| author | Font Llovet, Josep Maria |
| author2 | Rodríguez Pérez, Gonzalo |
| author2_role | author |
| author_browse | Font Llovet, Josep Maria Rodríguez Pérez, Gonzalo |
| author_facet | Font Llovet, Josep Maria Rodríguez Pérez, Gonzalo |
| author_role | author |
| collection | Dipòsit Digital de la UB |
| description | In [41 Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, .and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it . In [3] it is stated that this quasivariety is the variety of Sugihara algebras . Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same sense to the calculus Rof relevance logic, and we determine the totally ordered, the subdirectly irreducible, and the simple members of this variety, by using some consequences of the algebraizability of the logic RM (R-Mingle) with which they are associated . |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_1b424b46e522c115b2f7e92c8a2c2d92 |
| institution | Universidad de Barcelona |
| instname_str | Universidad de Barcelona |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:diposit.ub.edu:2445/132479 |
| publishDate | 1992 |
| publishDateSort | 1992 |
| publisher | Universitat Autònoma de Barcelona |
| publisherStr | Universitat Autònoma de Barcelona |
| reponame_str | Dipòsit Digital de la UB |
| spelling | A note on Sugihara algebras Font Llovet, Josep Maria Rodríguez Pérez, Gonzalo Àlgebra Anells (Àlgebra) Algebra Rings (Algebra) In [41 Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, .and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it . In [3] it is stated that this quasivariety is the variety of Sugihara algebras . Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same sense to the calculus Rof relevance logic, and we determine the totally ordered, the subdirectly irreducible, and the simple members of this variety, by using some consequences of the algebraizability of the logic RM (R-Mingle) with which they are associated . Universitat Autònoma de Barcelona https://hdl.handle.net/2445/132479 |
| spellingShingle | A note on Sugihara algebras Font Llovet, Josep Maria Àlgebra Anells (Àlgebra) Algebra Rings (Algebra) |
| status_str | publishedVersion |
| title | A note on Sugihara algebras |
| title_full | A note on Sugihara algebras |
| title_fullStr | A note on Sugihara algebras |
| title_full_unstemmed | A note on Sugihara algebras |
| title_short | A note on Sugihara algebras |
| title_sort | A note on Sugihara algebras |
| topic | Àlgebra Anells (Àlgebra) Algebra Rings (Algebra) |
| topic_facet | Àlgebra Anells (Àlgebra) Algebra Rings (Algebra) |
| url | https://hdl.handle.net/2445/132479 |