PL EN


Preferences help
enabled [disable] Abstract
Number of results
2010 | 45 |
Article title

On Frontal Heyting Algebras

Content
Title variants
Languages of publication
PL
Abstracts
PL
A frontal operator in a Heyting algebra is an expansive operator preserving finite meets which also satisfies the equation (x) ≤ y ∨ (y → x). A frontal Heyting algebra is a pair (H, ), where H is a Heyting algebra and a frontal operator on H. Frontal operators are always compatible, but not necessarily new or implicit in the sense of Caicedo and Cignoli (An algebraic approach to intuitionistic connectives. Journal of Symbolic Logic, 66, No4 (2001), 1620-1636). Classical examples of new implicit frontal operators are the functions, (op. cit., Example 3.1), the successor (op. cit., Example 5.2), and Gabbay’s operation (op. cit., Example 5.3). We study a Priestley duality for the category of frontal Heyting algebras and in particular for the varieties of Heyting algebras with each one of the implicit operations given as examples. The topological approach of the compatibility of operators seems to be important in the research of affin completeness of Heyting algebras with additional compatible operations. This problem have also a logical point of view. In fact, we look for some complete propositional intuitionistic calculus enriched with implicit connectives.
Keywords
PL
 
Publisher
Year
Volume
45
Physical description
Dates
published
2010
online
07 - 07 - 2015
References
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.ojs-issn-2084-2589-year-2010-volume-45-article-2870
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.