On Some Compatible Operations on Heyting Algebras

We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined...

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Autor principal: Ertola Biraben, Rodolfo Cristian
Otros Autores: San Martín, Hernán Javier
Formato: Artículo
Lenguaje:Inglés
Materias:
Acceso en línea:https://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdf
http://sedici.unlp.edu.ar/handle/10915/137724
https://link.springer.com/article/10.1007/s11225-011-9338-y
Aporte de:Registro referencial: Solicitar el recurso aquí
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100 |a Ertola Biraben, Rodolfo Cristian 
700 |a San Martín, Hernán Javier 
245 1 0 |a On Some Compatible Operations on Heyting Algebras 
041 7 |2 ISO 639-1  |a en 
300 |a  p.331-345 
520 3 |a We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. 
653 |a Intuitionistic logic 
653 |a Heyting algebra 
653 |a Compatible operation 
856 4 0 |u https://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdf 
856 4 1 |u http://sedici.unlp.edu.ar/handle/10915/137724 
856 4 1 |u https://link.springer.com/article/10.1007/s11225-011-9338-y 
952 |u https://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdf  |a MEMORIA ACADEMICA  |b MEMORIA ACADEMICA 
773 0 |7 nnas  |t Studia Logica.   |g Vol. 29 No. 3 (2011),331-345  |v 29  |l 3  |q 331-345  |d Berlin : Springer, 2011  |x ISSN 0039-3215  |k Article 
542 1 |f Esta obra está bajo una licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional  |u https://creativecommons.org/licenses/by-nc-sa/4.0/