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AN ALGEBRAIC APPROACH TO CANONICAL FORMULAS: INTUITIONISTIC CASE

Published online by Cambridge University Press:  05 October 2009

GURAM BEZHANISHVILI  and
NICK BEZHANISHVILI
GURAM BEZHANISHVILI*
Affiliation:
Department of Mathematical Sciences, New Mexico State University
NICK BEZHANISHVILI*
Affiliation:
Department of Computing, Imperial College London
*
*DEPARTMENT OF MATHEMATICAL SCIENCES, NEW MEXICO STATE UNIVERSITY, LAS CRUCES, NM 88003 E-mail:[email protected]
†DEPARTMENT OF COMPUTING, IMPERIAL COLLEGE LONDON, 180 QUEEN’S GATE, LONDON SW7 2AZ, UK E-mail:[email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 3 , September 2009 , pp. 517 - 549
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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