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  • 1
    Electronic Resource
    Electronic Resource
    Books received (1990)
    Springer
    Studia logica 49 (1990), S. 151-161 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00401560
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Axiomatic extensions of the constructive logic with strong negation and the disjunction property (1995)
    Springer
    Studia logica 55 (1995), S. 377-388 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract 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 εV, 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 σ−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 σ−1(W) have PQWC, there exist varietiesW of Heyting algebras having PQWC such that σ−1(W) contains infinitely many varieties (of Nelson algebras) with PQWC.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01057804
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  • 3
    Electronic Resource
    Electronic Resource
    Some investigations of varieties ofN-lattices-lattices (1984)
    Springer
    Studia logica 43 (1984), S. 257-280 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We examine some extensions of the constructive propositional logic with strong negation in the setting of varieties of $$\mathcal{N}$$ -lattices. The main aim of the paper is to give a description of all pretabular, primitive and preprimitive varieties of $$\mathcal{N}$$ -lattices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02429842
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  • 4
    Electronic Resource
    Electronic Resource
    Nelson algebras through Heyting ones: I (1990)
    Springer
    Studia logica 49 (1990), S. 105-126 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley ([15], [16]) for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described (Thm 2.3). The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction ([6], [25]) is also given (Thm 3.6). These results are applied to compare the equational category N of Nelson algebras and some its subcategories (and their duals) with the equational category H of Heyting algebras (and its dual). It is proved (Thm 4.1) that the category N is topological over the category H.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00401557
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