Bezhanishvili, GuramMoraschini, TommasoRaftery, James G.2017-10-312017-12Bezhanishvili, G., Moraschini, T. & Raftery, J.G. 2017, 'Epimorphisms in varieties of residuated structures', Journal of Algebra, vol. 492, pp. 185-211.0021-8693 (print)1090-266X (online)10.1016/j.jalgebra.2017.08.023http://hdl.handle.net/2263/62981It 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.en© 2017 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Journal of Air Transport Management. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Journal of Algebra, vol. 492, pp. 185-2011, 2017. doi : 10.1016/j.jalgebra.2017.08.023.Beth definabilityR-mingleRelevance logicIntuitionistic logicSubstructural logicSugihara monoidResiduated latticeEsakia spaceHeyting algebraBrouwerian algebraEpimorphismPostprint Article