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Decidable quasivarieties of p‐algebras

2025
journal article
article
10.1002/malq.202300064
Journal
Mathematical Logic Quarterly
100
Author
Kowalski Tomasz

Słomczyńska Katarzyna
Volume
71
Number
1
Article ID
2300064
ISSN
0942-5616
eISSN
1521-3870
Remarks

Online First 2025-02-10. Praca ta została zrealizowana w ramach grantu Narodowego Centrum Nauki OPUS-23 "Algebra and Substructural Logics: Fragments and Reducts", grant nr 2022/45/B/HS1/00606

Language
English
Journal language
English
Abstract in English

We show that for quasivarieties of p‐algebras the properties of (i) having decidable first‐order theory and (ii) having decidable first‐order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.

Affiliation
Wydział Filozoficzny : Instytut Filozofii
Scopus© citations
1
dc.abstract.enWe show that for quasivarieties of p‐algebras the properties of (i) having decidable first‐order theory and (ii) having decidable first‐order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.
dc.affiliationWydział Filozoficzny : Instytut Filozofii
dc.contributor.authorKowalski, Tomasz - 456998
dc.contributor.authorSłomczyńska, Katarzyna
dc.date.accessioned2025-03-21T11:56:35Z
dc.date.available2025-03-21T11:56:35Z
dc.date.createdat2025-02-27T11:00:03Zen
dc.date.issued2025
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.additionalOnline First 2025-02-10. Praca ta została zrealizowana w ramach grantu Narodowego Centrum Nauki OPUS-23 "Algebra and Substructural Logics: Fragments and Reducts", grant nr 2022/45/B/HS1/00606
dc.description.number1
dc.description.versionostateczna wersja wydawcy
dc.description.volume71
dc.identifier.articleid2300064
dc.identifier.doi10.1002/malq.202300064
dc.identifier.eissn1521-3870
dc.identifier.issn0942-5616
dc.identifier.project2022/45/B/HS1/00606
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/550552
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 4.0 Międzynarodowa
dc.rights.licenceCC-BY-NC-ND
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.pl
dc.share.typeotwarte czasopismo
dc.source.integratorfalse
dc.subtypeArticle
dc.titleDecidable quasivarieties of p‐algebras
dc.title.journalMathematical Logic Quarterly
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
We show that for quasivarieties of p‐algebras the properties of (i) having decidable first‐order theory and (ii) having decidable first‐order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones.
dc.affiliation
Wydział Filozoficzny : Instytut Filozofii
dc.contributor.author
Kowalski, Tomasz - 456998
dc.contributor.author
Słomczyńska, Katarzyna
dc.date.accessioned
2025-03-21T11:56:35Z
dc.date.available
2025-03-21T11:56:35Z
dc.date.createdaten
2025-02-27T11:00:03Z
dc.date.issued
2025
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.additional
Online First 2025-02-10. Praca ta została zrealizowana w ramach grantu Narodowego Centrum Nauki OPUS-23 "Algebra and Substructural Logics: Fragments and Reducts", grant nr 2022/45/B/HS1/00606
dc.description.number
1
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
71
dc.identifier.articleid
2300064
dc.identifier.doi
10.1002/malq.202300064
dc.identifier.eissn
1521-3870
dc.identifier.issn
0942-5616
dc.identifier.project
2022/45/B/HS1/00606
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/550552
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa - Użycie niekomercyjne - Bez utworów zależnych 4.0 Międzynarodowa
dc.rights.licence
CC-BY-NC-ND
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/legalcode.pl
dc.share.type
otwarte czasopismo
dc.source.integrator
false
dc.subtype
Article
dc.title
Decidable quasivarieties of p‐algebras
dc.title.journal
Mathematical Logic Quarterly
dc.type
JournalArticle
dspace.entity.typeen
Publication
Affiliations
Wydział Filozoficzny
Kowalski, Tomasz
philosophy
No affiliation
Słomczyńska, Katarzyna

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