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Varieties of positive modal algebras and structural completeness
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SYSNO ASEP 0504824 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Varieties of positive modal algebras and structural completeness Author(s) Moraschini, Tommaso (UIVT-O) SAI, RID Source Title Review of Symbolic Logic. - : Cambridge University Press - ISSN 1755-0203
Roč. 12, č. 3 (2019), s. 557-588Number of pages 32 s. Language eng - English Country GB - United Kingdom Keywords positive modal logic ; modal logic ; structural completeness ; admissible rule ; abstract algebraic logic ; algebraization of Gentzen systems Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GF15-34650L GA ČR - Czech Science Foundation (CSF) EF17_050/0008361 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Method of publishing Limited access Institutional support UIVT-O - RVO:67985807 UT WOS 000483091300006 EID SCOPUS 85067359071 DOI 10.1017/S1755020319000236 Annotation Positive modal algebras are the〈∧,∨, 3, D, 0, 1〉-subreducts of modal algebras. We show that the variety of positive interior algebras is not locally finite. However, the free one-generated positive interior algebra has 37 elements. Moreover, we show that there are exactly 16 varieties of height at most 4 in the lattice of varieties of positive interior algebras. Building on this, we infer that there are only 3 non-trivial structurally complete varieties of positive K4-algebras. These are also the unique non-trivial hereditarily structurally complete such varieties. Moreover, we characterize passively structurally complete varieties of positive K4-algebras and show that there are infinitely many of them. These results are related to the study of structurally complete axiomatic extensions of an algebraizable Gentzen system for positive modal logic. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1017/S1755020319000236
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