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Epimorphisms in Varieties of Residuated Structures
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SYSNO ASEP 0478590 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Epimorphisms in Varieties of Residuated Structures Tvůrce(i) Bezhanishvili, G. (US)
Moraschini, Tommaso (UIVT-O) SAI, RID
Raftery, J.G. (ZA)Zdroj.dok. Journal of Algebra. - : Elsevier - ISSN 0021-8693
Roč. 492, 15 December (2017), s. 185-211Poč.str. 27 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Epimorphism ; Brouwerian algebra ; Heyting algebra ; Esakia space ; Residuated lattice ; Sugihara monoid ; Substructural logic ; Intuitionistic logic ; Relevance logic ; R-mingle ; Beth definability Vědní obor RIV BA - Obecná matematika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA17-04630S GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000413129900011 EID SCOPUS 85031293860 DOI 10.1016/j.jalgebra.2017.08.023 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2018
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