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Epimorphisms in Varieties of Residuated Structures
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SYSNO ASEP 0478590 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Epimorphisms in Varieties of Residuated Structures Author(s) Bezhanishvili, G. (US)
Moraschini, Tommaso (UIVT-O) SAI, RID
Raftery, J.G. (ZA)Source Title Journal of Algebra. - : Elsevier - ISSN 0021-8693
Roč. 492, 15 December (2017), s. 185-211Number of pages 27 s. Language eng - English Country US - United States Keywords Epimorphism ; Brouwerian algebra ; Heyting algebra ; Esakia space ; Residuated lattice ; Sugihara monoid ; Substructural logic ; Intuitionistic logic ; Relevance logic ; R-mingle ; Beth definability Subject RIV BA - General Mathematics OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GA17-04630S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000413129900011 EID SCOPUS 85031293860 DOI 10.1016/j.jalgebra.2017.08.023 Annotation It is proved that epimorphisms are surjective in a range of varieties of residuated structures, including all varieties of Heyting or Brouwerian algebras of finite depth, and all varieties consisting of Gödel algebras, relative Stone algebras, Sugihara monoids or positive Sugihara monoids. This establishes the infinite deductive Beth definability property for a corresponding range of substructural logics. On the other hand, it is shown that epimorphisms need not be surjective in a locally finite variety of Heyting or Brouwerian algebras of width 2. It follows that the infinite Beth property is strictly stronger than the so-called finite Beth property, confirming a conjecture of Blok and Hoogland. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2018
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