Bibliography
Aczel, P. H. G.: 1980, ‘The Type Theoretic Interpretation of Constructive Set Theory, in A. Macintyre, L. Pacholski, and J. Paris (eds), Logic Colloquium 77, North-Holland Publ. Co., Amsterdam, pp. 55–66.
Beeson, M.: 1979, ‘Goodman's Theorem and Beyond’, Pacific Journal of Mathematics 84, 1–16.
Beeson, M.: 1979A, ‘A Theory of Constructions and Proofs’. Preprint no. 134, Department of Mathematics, Utrecht University.
Beeson, M.: 1980, ‘Recursive Models for Constructive Set Theories’. Preprint 129, Department of Mathematics, Utrecht University.
Bruijn, N. G. de: 1970, ‘The Mathematical Language AUTOMATH, Its Usage, and Some of Its Extensions’, in M. Laudet, D. lacombe, L. Nolin, and M. Schützenberger (eds), Symposium on Automatic Demonstration, Springer Verlag, Berlin, pp. 29–61.
Celluci, C.: 1981, ‘A Calculus of Constructions as a Representation of Intuitionistic Logical Proofs’, in S. Bernini (ed.), Atti del congresso nazionale di logica, Montecatini Terme, 1–5 ottobre 1979, Bibliopolis, Napoli, pp. 175–193
Curry, H. B., and R. Feys: 1957, Combinatory Logic I, North-Holland Publ. Co., Amsterdam.
Diller, J.: 1980, ‘Modified Realisation and the Formulae-as-Types Notion’, in J. P. Seldin, J. R. Hindley (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, New York, pp. 491–501.
Dummett, M. A. E.: 1977, Elements of Intuitionism, Clarendon Press, Oxford.
Feferman, S.: 1975, ‘A Language and Axioms for Explicit Mathematics’, in J. Crossley (ed.), Algebra and Logic, Springer, Berlin, pp. 87–139.
Feferman, S.: 1979, ‘Constructive Theories of Functions and Classes’, in M. Boffa, D. van Dalen and K. McAloon (eds.), Logic Colloquium 78, North-Holland, Amsterdam, pp. 159–224.
Gödel, K.: 1958, ‘Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica 12, 280–287.
Goodman, N.: 1970, ‘A Theory of Constructions Equivalent to Arithmetic’, in A. Kino, J. Myhill and R. E. Vesley (eds.), Intuitionism and Proof Theory, North-Holland Publ. Co., Amsterdam, pp. 101–120.
Hilbert D., and P. Bernays: 1934, Grundlagen der Mathematik I, Springer-Verlag, Berlin, 19682.
Heyting, A.: 1934, Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Springer, Berlin. Reprinted 1974.
Heyting, A.: 1956, Intuitionism, An Introduction, North-Holland Publ. Co., Amsterdam, 19662, 19713.
Heyting, A.: 1958, ‘Intuitionism in Mathematics’, in R. Klibansky (ed.) Philosophy in the Mid-century. A Survey, La nuova editrice, Firenza, pp. 101–115.
Heyting, A.: 1974, ‘Intuitionistic Views on the Nature of Mathematics’, Bolletino dell' Unione Mathematica Italiana (4)9, Supplemento, 122–134. Also in Synthese 27 1974, 79–81.
Howard, W. A.: 1980, ‘The Formulae-As-Types Notion of Construction’, in J. P. Seldin, and J. R. Hindley (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, London-New York, pp. 479–490.
Kleene, S. C.: 1945, ‘On the Interpretation of Intuitionistic Number Theory’, J. Symbolic Logic 10, 109–124.
Kleene, S. C.: 1960, ‘Realizability and Šanin's Algorithm for the Constructive Deciphering of Mathematical Sentences’, Logique et Analyse 3, 154–165.
Kleene, S. C. and R. E. Vesley: 1965, The Foundations of Intuitionistic Mathematics, North-Holland Publ. Co. Amsterdam.
Kleene, S. C.: 1973, ‘Realizability: A Retrospective Survey’, in A. R. D. Mathias and H. Rogers (eds.), Cambridge Summer School in Mathematical Logic, Springer, Berlin, pp. 95–112.
Kolmogorov, A. N.: 1932, ‘Zur Deutung der intuitionistischen Logik’, Math. Zeitschrift 35, 58–65.
Kreisel, G.: 1965, ‘Mathematical Logic’ in T. L. Saaty (ed.), Lectures on Modern Mathematics III, John Wiley & Sons, New York, pp. 95–195.
Kreisel, G.: 1970, ‘Church's Thesis: A Kind of Reducibility Axiom for Constructive Mathematics’, in A. Kino, J. Myhill and R. E. Vesley (eds.), Intuitionism and Proof Theory, North-Holland, Amsterdam, pp. 121–150.
Kreisel, G.: 1971, ‘A Survey of Proof Theory II’, in J. E. Fendstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, North-Holland, Amsterdam, pp. 109–170.
Läuchli, H.: 1970, ‘An Abstract Notion of Realizability for Which Intuitionistic Predicate Calculus is Complete’, in A. Kino, J. Myhill, and R. E. Vesley (eds.), Intuitionism and Proof theory, North-Holland Publ. Co., Amsterdam, pp. 227–234.
Martin-Löf, P.: 1975, ‘An intuitionistic Theory of Types: Predicative Part’, in H. E. Rose and J. C. Shepherdson (eds.), Logic colloquium '73, North-Holland Publ. Co., Amsterdam, pp. 73–118.
Martin-Löf, P: 1975A, ‘About Models for Intuitionistic Type Theories and the Notion of Definitional Equality’, in S. Kanger (ed.) Proceedings of the Third Scandinavian Logic Symposium, North-Holland Publ. Co., Amsterdam, pp. 81–109.
Martin-Löf, P.: 1982, ‘Constructive Mathematics and Computer Programming’. Reports of the Dept. of Mathematics, University of Stockholm, 1979, no. 11. Appeared in L. S. Cohen, J. Los, H. Pfeiffer and K. P. Podewski (eds.), Logic, Methodology and Philosophy of Science VI, North-Holland Publ. Co., Amsterdam, pp. 153–175.
Pitts, A. M.: 1981, ‘The Theory of Triposes’, Ph.D. thesis, Cambridge University, U.K.
Šanin, N. A.: 1958, ‘On the Constructive Interpretation of Mathematical Judgments’, Trudy Mat. Inst. Steklov 52, 226–311 (Russian). English translation: Am. Math. Soc. Transl. (2) 23 (1963), 109–189.
Scott, D. A.: 1970, ‘Constructive Validity’, in M. Laudet, D. Lacombe, L. Nolin, and M. Schützenberger (eds.), Symposium on Automatic Demonstration, Springer Verlag, Berlin, pp. 237–275.
Sundholm, G.: 1983, ‘Constructions, Proofs and the Meaning of Logical Constants’, J. Philosophical Logic 12, 151–172.
Troelstra, A. S.: 1973, Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Springer, Berlin, Ch. I–IV.
Troelstra, A. S.: 1977, ‘A Note on Non-extensional Operations in Connection with Continuity and Recursiveness’, Indag. Math, 39, 455–462.
Troelstra, A. S.: 1980, ‘The Interplay between Logic and Mathematics: Intuitionism’, in E. Agazzi (ed.), Modern Logic — A Survey, D. Reidel, Dordrecht, pp. 197–221.
van Dalen, D.: 1973, ‘Lectures on Intuitionism’, in A. R. D. Mathias and H. Rogers (eds.), Cambridge Summer School in Mathematical Logic. Springer, Berlin, pp. 1–94.
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Diller, J., Troelstra, A.S. Realizability and intuitionistic logic. Synthese 60, 253–282 (1984). https://doi.org/10.1007/BF00485463
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DOI: https://doi.org/10.1007/BF00485463