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AN ALGEBRAIC APPROACH TO CANONICAL FORMULAS: INTUITIONISTIC CASE.
- Source :
-
Review of Symbolic Logic . Sep2009, Vol. 2 Issue 3, p517-549. 33p. 6 Diagrams. - Publication Year :
- 2009
-
Abstract
- We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (⋀,→) homomorphisms, (⋀,→, 0) homomorphisms, and (⋀,→⋁,) homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschev's subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we obtain a new simplified proof (which is algebraic in nature) of Zakharyaschev's theorem that each intermediate logic can be axiomatized by canonical formulas. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17550203
- Volume :
- 2
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Review of Symbolic Logic
- Publication Type :
- Academic Journal
- Accession number :
- 45386257
- Full Text :
- https://doi.org/10.1017/S1755020309990177