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  1. Notes on Constructive Negation.Grigori Mints - 2006 - Synthese 148 (3):701-717.
    We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, we (...)
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  • Dual realizability in symmetric logic.I. D. Zaslavsky - 2001 - Annals of Pure and Applied Logic 113 (1-3):389-397.
    A variant of the notion of symmetric constructive realizability is introduced where the information about the symmetric constructive truth or falsity of an arithmetical formula is expressed by a single natural number. The methods of transformations of such a realization to the realizations of known kinds and those of reverse transformations are given. The formal arithmetical system based on such a realizability is investigated.
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