Propositional calculus and realizability
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References
- Alonzo Church, A set of postulates for the foundation of logic, Ann. of Math. (2) 33 (1932), no. 2, 346–366. MR 1503059, DOI 10.2307/1968337 Gerhard Gentzen, Untersuchungen über das logische Schliessen, Math. Zeit. vol. 39 (1934-1935) pp. 176-210, 405-431. V. Glivenko, Sur quelques points de la logique de M. Brouwer, Bulletin de la Classe des Sciences de l’Académie Royale de Belgique (5) vol. 15 (1929) pp. 183-188.
- Kurt Gödel, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatsh. Math. Phys. 37 (1930), no. 1, 349–360 (German). MR 1549799, DOI 10.1007/BF01696781
- Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692 —, Zum intuitionistischen Aussagenkalül, Ergebnisse eines Mathematischen Kolloquiums, no. 4 (for 1931-1932, published 1933), p. 40.
- Leon Henkin, An algebraic characterization of quantifiers, Fund. Math. 37 (1950), 63–74. MR 40234, DOI 10.4064/fm-37-1-63-74 Arend Heyting, Die formalen Regeln der intuitionistischen Logik, Preuss. Akad. Wiss. Sitzungsber. (1930) pp. 42-56. —, Die formalen Regeln der intuitionistischen Mathematik, Ibid. pp. 57-71, 158-169. Stanisław Jaśkowski, Recherches sur le système de la logique intuitioniste, Actes du Congrès International de Philosophie Scientifique VI, Philosophie des mathématiques, Actualités Scientifiques et Industrielles, no. 393, Paris, Hermann, 1936, pp. 58-61. S. C. Kleene, On notation for ordinal numbers, J. Symbolic Logic vol. 3 (1938) pp. 150-155.
- S. C. Kleene, Recursive predicates and quantifiers, Trans. Amer. Math. Soc. 53 (1943), 41–73. MR 7371, DOI 10.1090/S0002-9947-1943-0007371-8
- S. C. Kleene, On the interpretation of intuitionistic number theory, J. Symbolic Logic 10 (1945), 109–124. MR 15346, DOI 10.2307/2269016
- S. C. Kleene, On the intuitionistic logic, Library of the Tenth International Congress of Philosophy, Amsterdam, August 11–18, 1948, Vol. I, Proceedings of the Congress, publisher unknown, 1949, pp. 741–743. MR 0027236
- S. C. Kleene, A symmetric form of Gödel’s theorem, Nederl. Akad. Wetensch., Proc. 53 (1950), 800–802 = Indagationes Math. 12, 244–246 (1950). MR 36191 —, Recursive functions and intuitionistic mathematics, Proceedings of the International Congress of Mathematicians (Cambridge, Mass., Aug. 30-Sept. 6, 1950).
- Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790 Leopold Löwenheim, Über Möglichkeiten im Relativkalkül, Math. Ann. vol. 76 (1915) pp. 447-470. Jan Łukasiewicz, O logice trójwartościowej (On three-valued logic), Ruch filozoficzny (Lwów) vol. 5 (1920) pp. 169-171. Jan Łukasiewicz and Alfred Tarski, Untersuchungen über den Aussagenkalkül, Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Cl. III, vol. 23 (1930) pp. 30-50.
- J. C. C. McKinsey and Alfred Tarski, Some theorems about the sentential calculi of Lewis and Heyting, J. Symbolic Logic 13 (1948), 1–15. MR 24396, DOI 10.2307/2268135
- Andrzej Mostowski, Proofs of non-deducibility in intuitionistic functional calculus, J. Symbolic Logic 13 (1948), 204–207. MR 28257, DOI 10.2307/2267135
- David Nelson, Recursive functions and intuitionistic number theory, Trans. Amer. Math. Soc. 61 (1947), 307–368. MR 25420, DOI 10.1090/S0002-9947-1947-0025420-1
- Emil L. Post, Introduction to a General Theory of Elementary Propositions, Amer. J. Math. 43 (1921), no. 3, 163–185. MR 1506440, DOI 10.2307/2370324 Thoralf Skolem, Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre, Wissenschaftliche Vorträge gehalten auf dem Fünften Kongress der Skandinavischen Mathematiker in Helsingfors vom 4. bis 7. Juli 1922, Helsingfors, 1923, pp. 217-232.
Additional Information
- © Copyright 1953 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 75 (1953), 1-19
- MSC: Primary 02.0X
- DOI: https://doi.org/10.1090/S0002-9947-1953-0055952-4
- MathSciNet review: 0055952