Axiomatic extensions of the constructive logic with strong negation and the disjunction property

Studia Logica 55 (3):377 - 388 (1995)
We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B V, thenA×B is a homomorphic image of some well-connected algebra ofV.We prove:• each varietyV of Nelson algebras with PQWC lies in the fibre –1(W) for some varietyW of Heyting algebras having PQWC, • for any varietyW of Heyting algebras with PQWC the least and the greatest varieties in –1(W) have PQWC, • there exist varietiesW of Heyting algebras having PQWC such that –1(W) contains infinitely many varieties (of Nelson algebras) with PQWC.
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DOI 10.1007/BF01057804
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References found in this work BETA
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
A Result on Propositional Logics Having the Disjunction Property.Robert E. Kirk - 1982 - Notre Dame Journal of Formal Logic 23 (1):71-74.

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On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.

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