A NOTE ON SUGIHARA ALGEBRAS

In [4] 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...

Full description

Saved in:
Bibliographic Details
Published in:Publicacions matemàtiques 1992-01, Vol.36 (2A), p.591-599
Main Authors: Font, Josep M., Pérez, Gonzalo Rodríguez
Format: Article
Language:English
Subjects:
Abstract algebra
Algebra
Anells (Àlgebra)
Axioms
Logical theorems
Mathematical theorems
Relevance logic
Rings (Algebra)
Semantics
Semigroups
Typographic fonts
Universal algebra
Àlgebra
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c2339-42c66bb6e233c3200d788dd11658705cd97539e7df473c92617af36f967ad7353
cites
container_end_page 599
container_issue 2A
container_start_page 591
container_title Publicacions matemàtiques
container_volume 36
creator Font, Josep M.
Pérez, Gonzalo Rodríguez
description In [4] 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 R of 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.
doi_str_mv 10.5565/PUBLMAT_362A92_19
format article
fullrecord <record><control><sourceid>jstor_latin</sourceid><recordid>TN_cdi_latinindex_primary_oai_record_407291</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>43736389</jstor_id><sourcerecordid>43736389</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2339-42c66bb6e233c3200d788dd11658705cd97539e7df473c92617af36f967ad7353</originalsourceid><addsrcrecordid>eNplkFtLAzEQhYMoWKs_QETYd1lNMrlsHtNS28LaSi_PIU2ysKV2Jamg_94tq0XwYZg5zPnOw0HoluBHzgV_el0Pyhe9MiCoVtQQdYZ6FBOWM-D4HPUwbW_CFFyiq5S2GNOiwKyH7nQ2m69G2XyWLdfj6UQvdKbL8Wiw0MtrdFHZXQo3P7uP1s-j1XCSl_PxdKjL3FEAlTPqhNhsRGiVA4qxl0XhPSGCFxJz55XkoIL0FZPgFBVE2gpEpYS0XgKHPnrocnf2UO_rvQ-f5j3WbzZ-mcbWJgbXRG8YllSR1k06t0sf7vgL0dnDr7ETx6Gt3QBnBcV_mNikFEN1yifYHPsz__prmfuO2aZDE08AAwkCCgXfT-NoSA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A NOTE ON SUGIHARA ALGEBRAS</title><source>JSTOR Archival Journals and Primary Sources Collection</source><creator>Font, Josep M. ; Pérez, Gonzalo Rodríguez</creator><creatorcontrib>Font, Josep M. ; Pérez, Gonzalo Rodríguez</creatorcontrib><description>In [4] 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 R of 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.</description><identifier>ISSN: 0214-1493</identifier><identifier>EISSN: 2014-4350</identifier><identifier>DOI: 10.5565/PUBLMAT_362A92_19</identifier><language>eng</language><publisher>Universitat Autònoma de Barcelona</publisher><subject>Abstract algebra ; Algebra ; Anells (Àlgebra) ; Axioms ; Logical theorems ; Mathematical theorems ; Relevance logic ; Rings (Algebra) ; Semantics ; Semigroups ; Typographic fonts ; Universal algebra ; Àlgebra</subject><ispartof>Publicacions matemàtiques, 1992-01, Vol.36 (2A), p.591-599</ispartof><rights>(c) Universitat Autònoma de Barcelona, 1992 info:eu-repo/semantics/openAccess</rights><rights>free</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2339-42c66bb6e233c3200d788dd11658705cd97539e7df473c92617af36f967ad7353</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/43736389$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/43736389$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,885,4024,27923,27924,27925,58238,58471</link.rule.ids></links><search><creatorcontrib>Font, Josep M.</creatorcontrib><creatorcontrib>Pérez, Gonzalo Rodríguez</creatorcontrib><title>A NOTE ON SUGIHARA ALGEBRAS</title><title>Publicacions matemàtiques</title><description>In [4] 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 R of 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.</description><subject>Abstract algebra</subject><subject>Algebra</subject><subject>Anells (Àlgebra)</subject><subject>Axioms</subject><subject>Logical theorems</subject><subject>Mathematical theorems</subject><subject>Relevance logic</subject><subject>Rings (Algebra)</subject><subject>Semantics</subject><subject>Semigroups</subject><subject>Typographic fonts</subject><subject>Universal algebra</subject><subject>Àlgebra</subject><issn>0214-1493</issn><issn>2014-4350</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNplkFtLAzEQhYMoWKs_QETYd1lNMrlsHtNS28LaSi_PIU2ysKV2Jamg_94tq0XwYZg5zPnOw0HoluBHzgV_el0Pyhe9MiCoVtQQdYZ6FBOWM-D4HPUwbW_CFFyiq5S2GNOiwKyH7nQ2m69G2XyWLdfj6UQvdKbL8Wiw0MtrdFHZXQo3P7uP1s-j1XCSl_PxdKjL3FEAlTPqhNhsRGiVA4qxl0XhPSGCFxJz55XkoIL0FZPgFBVE2gpEpYS0XgKHPnrocnf2UO_rvQ-f5j3WbzZ-mcbWJgbXRG8YllSR1k06t0sf7vgL0dnDr7ETx6Gt3QBnBcV_mNikFEN1yifYHPsz__prmfuO2aZDE08AAwkCCgXfT-NoSA</recordid><startdate>19920101</startdate><enddate>19920101</enddate><creator>Font, Josep M.</creator><creator>Pérez, Gonzalo Rodríguez</creator><general>Universitat Autònoma de Barcelona</general><general>Universitat Autònoma de Barcelona: Servei de Publicacions</general><scope>AAYXX</scope><scope>CITATION</scope><scope>XX2</scope><scope>77F</scope></search><sort><creationdate>19920101</creationdate><title>A NOTE ON SUGIHARA ALGEBRAS</title><author>Font, Josep M. ; Pérez, Gonzalo Rodríguez</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2339-42c66bb6e233c3200d788dd11658705cd97539e7df473c92617af36f967ad7353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>Abstract algebra</topic><topic>Algebra</topic><topic>Anells (Àlgebra)</topic><topic>Axioms</topic><topic>Logical theorems</topic><topic>Mathematical theorems</topic><topic>Relevance logic</topic><topic>Rings (Algebra)</topic><topic>Semantics</topic><topic>Semigroups</topic><topic>Typographic fonts</topic><topic>Universal algebra</topic><topic>Àlgebra</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Font, Josep M.</creatorcontrib><creatorcontrib>Pérez, Gonzalo Rodríguez</creatorcontrib><collection>CrossRef</collection><collection>Recercat</collection><collection>Latindex</collection><jtitle>Publicacions matemàtiques</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Font, Josep M.</au><au>Pérez, Gonzalo Rodríguez</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A NOTE ON SUGIHARA ALGEBRAS</atitle><jtitle>Publicacions matemàtiques</jtitle><date>1992-01-01</date><risdate>1992</risdate><volume>36</volume><issue>2A</issue><spage>591</spage><epage>599</epage><pages>591-599</pages><issn>0214-1493</issn><eissn>2014-4350</eissn><abstract>In [4] 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 R of 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.</abstract><pub>Universitat Autònoma de Barcelona</pub><doi>10.5565/PUBLMAT_362A92_19</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0214-1493
ispartof Publicacions matemàtiques, 1992-01, Vol.36 (2A), p.591-599
issn 0214-1493
2014-4350
language eng
recordid cdi_latinindex_primary_oai_record_407291
source JSTOR Archival Journals and Primary Sources Collection
subjects Abstract algebra
Algebra
Anells (Àlgebra)
Axioms
Logical theorems
Mathematical theorems
Relevance logic
Rings (Algebra)
Semantics
Semigroups
Typographic fonts
Universal algebra
Àlgebra
title A NOTE ON SUGIHARA ALGEBRAS
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T17%3A44%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_latin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20NOTE%20ON%20SUGIHARA%20ALGEBRAS&rft.jtitle=Publicacions%20matem%C3%A0tiques&rft.au=Font,%20Josep%20M.&rft.date=1992-01-01&rft.volume=36&rft.issue=2A&rft.spage=591&rft.epage=599&rft.pages=591-599&rft.issn=0214-1493&rft.eissn=2014-4350&rft_id=info:doi/10.5565/PUBLMAT_362A92_19&rft_dat=%3Cjstor_latin%3E43736389%3C/jstor_latin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2339-42c66bb6e233c3200d788dd11658705cd97539e7df473c92617af36f967ad7353%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=43736389&rfr_iscdi=true