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Epimorphisms in Varieties of Residuated Structures

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    0478590 - ÚI 2018 RIV US eng J - Journal Article
    Bezhanishvili, G. - Moraschini, Tommaso - Raftery, J.G.
    Epimorphisms in Varieties of Residuated Structures.
    Journal of Algebra. Roč. 492, 15 December (2017), s. 185-211. ISSN 0021-8693. E-ISSN 1090-266X
    R&D Projects: GA ČR GA17-04630S
    Institutional support: RVO:67985807
    Keywords : Epimorphism * Brouwerian algebra * Heyting algebra * Esakia space * Residuated lattice * Sugihara monoid * Substructural logic * Intuitionistic logic * Relevance logic * R-mingle * Beth definability
    OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    Impact factor: 0.675, year: 2017

    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.
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