On Some Compatible Operations on Heyting Algebras

Studia Logica 98 (3):331-345 (2011)
Abstract
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
Keywords Intuitionistic logic  Heyting algebra  compatible operation
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,399
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
Citations of this work BETA

No citations found.

Similar books and articles
Vann McGee (1996). Logical Operations. Journal of Philosophical Logic 25 (6):567 - 580.
K. Britz (1999). A Power Algebra for Theory Change. Journal of Logic, Language and Information 8 (4):429-443.
Denis Bonnay (2006). Logicality and Invariance. Bulletin of Symbolic Logic 14 (1):29-68.
Analytics

Monthly downloads

Added to index

2011-08-12

Total downloads

14 ( #116,050 of 1,102,971 )

Recent downloads (6 months)

4 ( #84,832 of 1,102,971 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.