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Notes on constructive negation

Synthese 148 (3):701 - 717 (2006)

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  1. Einführung in die operative Logik und Mathematik.Paul Lorenzen - 1955 - Berlin,: Springer.
    in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...)
  • The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
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  • Non-Null implication.David Nelson - 1966 - Journal of Symbolic Logic 31 (4):562-572.
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  • The Theory of Algorithms.A. A. Markov - 1953 - Journal of Symbolic Logic 18 (4):340-341.
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  • A negationless interpretation of intuitionistic theories.Victor N. Krivtsov - 2000 - Erkenntnis 53 (1-2):155-179.
    In a seriesof papers beginning in 1944, the Dutch mathematician and philosopherGeorge Francois Cornelis Griss proposed that constructivemathematics should be developedwithout the use of the intuitionistic negation1 and,moreover, without any use of a nullpredicate.In the present work, we give formalized versions of intuitionisticarithmetic, analysis,and higher-order arithmetic in the spirit ofGriss' ``negationless intuitionistic mathematics''and then consider their relation to thecurrent formalizations of thesetheories.
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  • Mathematical significance of consistency proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (2):155-182.
  • On the interpretation of intuitionistic number theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
  • Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
    Provability, Computability and Reflection.
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  • An Approach to Constructive Mathematical Logic.A. A. Markov, B. van Rootselaar & J. F. Staal - 1975 - Journal of Symbolic Logic 40 (1):85-85.