{"title":"Decidable varieties of p-algebras","authors":"Tomasz Kowalski, Katarzyna Słomczyńska","doi":"arxiv-2409.09015","DOIUrl":null,"url":null,"abstract":"We show that for quasivarieties of p-algebras the properties of (i) having\ndecidable first-order theory and (ii) having decidable first-order theory of\nthe finite members, coincide. The only two quasivarieties with these properties\nare the trivial variety and the variety of Boolean algebras. This contrasts\nsharply, even for varieties, with the situation in Heyting algebras where\ndecidable varieties do not coincide with finitely decidable ones.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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