Linked bibliography for the SEP article "Intuitionistic Logic" by Joan Moschovakis

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Aczel, P., 1968, “Saturated intuitionistic theories,” in H.A. Schmidt, K. Schütte, and H.-J. Thiele (eds.), Contributions to Mathematical Logic, Amsterdam: North-Holland: 1–11. (Scholar)
Artemov, S. and Iemhoff, R., 2007, “The basic intuitionistic logic of proofs,” Journal of Symbol Logic, 72: 439–451. (Scholar)
Avigad, J. and Feferman, S., 1998, “Gödel’s functional (”Dialectica“) interpretation,” Chapter V of Buss (ed.) 1998: 337–405.
Bar-Hillel, Y. (ed.), 1965, Logic, Methodology and Philosophy of Science, Amsterdam: North Holland. (Scholar)
Beeson, M. J., 1985, Foundations of Constructive Mathematics, Berlin: Springer. (Scholar)
Benacerraf, P. and Hilary Putnam (eds.), 1983, Philosophy of Mathematics: Selected Readings, 2nd Edition, Cambridge: Cambridge University Press. (Scholar)
Beth, E. W., 1956, “Semantic construction of intuitionistic logic,” Koninklijke Nederlandse Akad. von Wettenscappen, 19(11): 357–388. (Scholar)
Brauer, E., 2022, “The modal logic of potential infinity: convergent versus branching possibilities,” Erkenntnis 87:2161–2179. (Scholar)
Brauer, E., Linnebo O. and Shapiro, S., 2022, “Divergent potentialism: a modal analysis with an application to choice sequences,” Philosophia Mathematica 30(2): 143–172. (Scholar)
Brouwer, L. E. J., 1907, “On the Foundations of Mathematics,” Thesis, Amsterdam; English translation in Heyting (ed.) 1975: 11–101. (Scholar)
–––, 1908, “The Unreliability of the Logical Principles,” English translation in Heyting (ed.) 1975: 107–111. (Scholar)
–––, 1912, “Intuitionism and Formalism,” English translation by A. Dresden, Bulletin of the American Mathematical Society, 20 (1913): 81–96, reprinted in Benacerraf and Putnam (eds.) 1983: 77–89; also reprinted in Heyting (ed.) 1975: 123–138. (Scholar)
–––, 1923 [1954], “On the significance of the principle of excluded middle in mathematics, especially in function theory,” “Addenda and corrigenda,” and “Further addenda and corrigenda,” English translation in van Heijenoort (ed.) 1967: 334–345. (Scholar)
–––, 1923C, “Intuitionistische Zerlegung mathematischer Grundbegriffe,” Jahresbericht der Deutschen Mathematiker-Vereinigung, 33 (1925): 251–256; reprinted in Heyting (ed.) 1975, 275–280. (Scholar)
–––, 1927, “Intuitionistic reflections on formalism,” originally published in 1927, English translation in van Heijenoort (ed.) 1967: 490–492. (Scholar)
–––, 1948, “Consciousness, philosophy and mathematics,” originally published (1948), reprinted in Benacerraf and Putnam (eds.) 1983: 90–96. (Scholar)
Burr, W., 2004, “The intuitionistic arithmetical hierarchy,” in J. van Eijck, V. van Oostrom and A. Visser (eds.), Logic Colloquium ’99 (Lecture Notes in Logic 17), Wellesley, MA: ASL and A. K. Peters, 51–59. (Scholar)
Buss, S. (ed.), 1998, Handbook of Proof Theory, Amsterdam and New York: Elsevier. (Scholar)
Chen, R-M. and Rathjen, M., 2012, “Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory,” Archive for Mathematical Logic, 51: 789–818. (Scholar)
Colacito, A., de Jongh, D. and Vargas, A., 2017, “Subminimal Negation”, Soft Computing, 21: 165–164. (Scholar)
Crossley, J., and M. A. E. Dummett (eds.), 1965, Formal Systems and Recursive Functions, Amsterdam: North-Holland Publishing. (Scholar)
van Dalen, D. (ed.), 1981, Brouwer’s Cambridge Lectures on Intuitionism, Cambridge: Cambridge University Press. (Scholar)
Dummett, M., 1975, “The philosophical basis of intuitionistic logic,” originally published (1975), reprinted in Benacerraf and Putnam (eds.) 1983: 97–129. (Scholar)
Dyson, V. and Kreisel, G., 1961, Analysis of Beth’s semantic construction of intuitionistic logic, Technical Report No. 3, Stanford: Applied Mathematics and Statistics Laboratory, Stanford University. (Scholar)
Ewald, W. B., 1986, “Intuitionistic tense and modal logic,” Journal of Symbolic Logic 51(1): 166–179. (Scholar)
Ferreira, F., 2008, “A most artistic package of a jumble of ideas,” Dialectica, 62: 205–222.
Fitting, M., 1987, “Resolution for intuitionistic logic”, Proceedings of the Second International Symposium on Methodologies for Intelligent Systems, December 1987: 400–407. (Scholar)
Friedman, H., 1975, “The disjunction property implies the numerical existence property,” Proceedings of the National Academy of Science, 72: 2877–2878. (Scholar)
Gentzen, G., 1934–5, “Untersuchungen Über das logische Schliessen,” Mathematische Zeitschrift, 39: 176–210, 405–431. (Scholar)
Ghilardi, S., 1999, “Unification in intuitionistic logic,” Journal of Symbolic Logic, 64: 859–880. (Scholar)
Glivenko, V., 1929, “Sur quelques points de la logique de M. Brouwer,” Académie Royale de Belgique, Bulletins de la classe des sciences, 5 (15): 183–188. (Scholar)
Gödel, K., 1932, “Zum intuitionistischen Aussagenkalkül,” Anzeiger der Akademie der Wissenschaften in Wien, 69: 65–66. Reproduced and translated with an introductory note by A. S. Troelstra in Gödel 1986: 222–225. (Scholar)
–––, 1933e, “Zur intuitionistischen Arithmetik und Zahlentheorie,” Ergebnisse eines mathematischen Kolloquiums, 4: 34–38. (Scholar)
–––, 1933f, “Eine Interpretation des intuitionistischen Aussagenkalküls,” reproduced and translated with an introductory note by A. S. Troelstra in Gödel 1986: 296–304. (Scholar)
–––, 1958, “Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes,” Dialectica, 12: 280–287. Reproduced with an English translation in Gödel 1990: 241–251. (Scholar)
–––, 1986, Collected Works, Vol. I, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
–––, 1990, Collected Works, Vol. II, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
Goudsmit, J. P., 2015, Intuitionistic Rules: Admissible Rules of Intermediate Logics, Ph.D. dissertation, University of Utrecht. (Scholar)
Harrop R., 1960, “Concerning formulas of the types \(A \rightarrow B \vee C, A \rightarrow (Ex)B(x)\) in intuitionistic formal systems,” Journal of Symbolic Logic, 25: 27–32. (Scholar)
van Heijenoort, J. (ed.), 1967, From Frege to Gödel: A Source Book In Mathematical Logic 1879–1931, Cambridge, MA: Harvard University Press. (Scholar)
Heyting, A., 1930, “Die formalen Regeln der intuitionistischen Logik,” in three parts, Sitzungsberichte der preussischen Akademie der Wissenschaften: 42–71, 158–169. English translation of Part I in Mancosu 1998: 311–327. (Scholar)
–––, 1956, Intuitionism: An Introduction, Amsterdam: North-Holland Publishing, 3rd revised edition, 1971. (Scholar)
Heyting, A. (ed.), 1975, L. E. J. Brouwer: Collected Works (Volume 1: Philosophy and Foundations of Mathematics), Amsterdam and New York: Elsevier. (Scholar)
Howard, W. A., 1973, “Hereditarily majorizable functionals of finite type,” in Troelstra (ed.) 1973: 454–461. (Scholar)
Hyland, J. M. E., 1982, “The effective topos,” in Troelstra and van Dalen (ed.) 1982: 165–216. (Scholar)
Iemhoff, R., 2001, “On the admissible rules of intuitionistic propositional logic,” Journal of Symbolic Logic, 66: 281–294. (Scholar)
–––, 2005, “Intermediate logics and Visser’s rules,” Notre Dame Journal of Formal Logic, 46: 65–81. (Scholar)
Iemhoff, R. and Metcalfe, G., 2009, “Proof theory for admissible rules,” Annals of Pure and Applied Logic, 159: 171–186. (Scholar)
Jankov, V. A., 1968, “The construction of a sequence of strongly independent superintuitionistic propositional calculii,” Soviet Math. Doklady, 9: 801–807. (Scholar)
Jerabek, E., 2008, “Independent bases of admissible rules,” Logic Journal of the IGPL, 16: 249–267. (Scholar)
de Jongh, D. H. J., 1970, “The maximality of the intuitionistic propositional calculus with respect to Heyting’s Arithmetic,” Journal of Symbolic Logic, 6: 606. (Scholar)
de Jongh, D. H. J., and Smorynski, C., 1976, “Kripke models and the intuitionistic theory of species,” Annals of Mathematical Logic, 9: 157–186. (Scholar)
de Jongh, D., Verbrugge, R. and Visser, A., 2011, “Intermediate logics and the de Jongh property,” Archive for Mathematical Logic, 50: 197–213. (Scholar)
Kino, A., Myhill, J. and Vesley, R. E. (eds.), 1970, Intuitionism and Proof Theory: Proceedings of the summer conference at Buffalo, NY, 1968, Amsterdam: North-Holland. (Scholar)
Kleene, S. C., 1945, “On the interpretation of intuitionistic number theory,” Journal of Symbolic Logic, 10: 109–124. (Scholar)
–––, 1952, Introduction to Metamathematics, Princeton: Van Nostrand. (Scholar)
–––, 1962, “Disjunction and existence under implication in elementary intuitionistic formalisms,” Journal of Symbolic Logic, 27: 11–18. (Scholar)
–––, 1963, “An addendum,” Journal of Symbolic Logic, 28: 154–156. (Scholar)
–––, 1965, “Classical extensions of intuitionistic mathematics,” in Bar-Hillel (ed.) 1965: 31–44. (Scholar)
–––, 1969, Formalized Recursive Functionals and Formalized Realizability, Memoirs of the American Mathematical Society 89. (Scholar)
Kleene, S. C. and Vesley, R. E., 1965, The Foundations of Intuitionistic Mathematics, Especially in Relation to Recursive Functions, Amsterdam: North-Holland. (Scholar)
Kreisel, G., 1958, “Elementary completeness properties of intuitionistic logic with a note on negations of prenex formulas,” Journal of Symbolic Logic, 23: 317–330. (Scholar)
–––, 1962, “On weak completeness of intuitionistic predicate logic,” Journal of Symbolic Logic, 27: 139–158. (Scholar)
Kripke, S. A., 1965, “Semantical analysis of intuitionistic logic,” in J. Crossley and M. A. E. Dummett (eds.) 1965: 92–130. (Scholar)
–––, 2019, “Free choice sequences: A temporal interpretation compatible with acceptance of classical mathematics,” Indag.Math., 30: 492–499. (Scholar)
Krol, M., 1978, “A topological model of intuitionistic analysis with Kripke’s Schema,” Zeitschrift für Math. Logik und Grundlagen der Math., 24: 427–436. (Scholar)
Leivant, D., 1979, “Maximality of Intuitionistic Logic,” Mathematical Centre Tracts 73, Mathematisch Centrum, Amsterdam. (Scholar)
–––, 1985, “Syntactic translations and provably recursive functions,” Journal of Symbolic Logic, 50: 682–688. (Scholar)
Läuchli, H., 1970, “An abstract notion of realizability for which intuitionistic predicate calculus is complete,” in A. Kino et al. (eds.) 1965: 227–234. (Scholar)
Lifschitz, V., 1979, “CT\(_0\) is stronger than CT\(_0\)!,” Proceedings of the American Mathematical Society, 73(1): 101–106.
Mancosu, P., 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, New York and Oxford: Oxford University Press. (Scholar)
Martin-Löf, P., 1984, Intuitionistic Type Theory, Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980, Napoli: Bibliopolis. (Scholar)
Mints, G., 2012, “The Gödel–Tarski translations of intuitionistic propositional formulas,” in Correct Reasoning (Lecture Notes in Computer Science 7265), E. Erdem et al. (eds.), Dordrecht: Springer-Verlag: 487–491. (Scholar)
Mints, G., Olkhovikov, G. and Urquhart, A., 2013, “Failure of interpolation in the intuitionistic logic of constant domains,” Journal of Symbolic Logic 78(3): 937–950. (Scholar)
Moschovakis, J. R., 1971, “Can there be no nonrecursive functions?,” Journal of Symbolic Logic, 36: 309–315. (Scholar)
–––, 2003, “Classical and constructive hierarchies in extended intuitionistic analysis,” Journal of Symbolic Logic, 68: 1015–1043. (Scholar)
–––, 2009, “The logic of Brouwer and Heyting,” in Logic from Russell to Church (Handbook of the History of Logic, Volume 5), J. Woods and D. Gabbay (eds.), Amsterdam: Elsevier: 77–125. (Scholar)
–––, 2017, “Intuitionistic analysis at the end of time,” Bulletin of Symbolic Logic, 23: 279–295. (Scholar)
Myhill, J., 1967, “Notes toward an axiomatization of intuitionistic analysis,” Logique et Analyse 9: 280–297. (Scholar)
Nelson, D., 1947, “Recursive functions and intuitionistic number theory,” Transactions of the American Mathematical Society, 61: 307–368. (Scholar)
Nishimura, I., 1960, “On formulas of one variable in intuitionistic propositional calculus,” Journal of Symbolic Logic, 25: 327–331. (Scholar)
van Oosten, J., 1991, “A semantical proof of de Jongh’s theorem,” Archives for Mathematical Logic, 31: 105–114. (Scholar)
–––, 2002, “Realizability: a historical essay,” Mathematical Structures in Computer Science, 12: 239–263. (Scholar)
–––, 2008, Realizability: An Introduction to its Categorical Side, Amsterdam: Elsevier. (Scholar)
Plisko, V. E., 1992, “On arithmetic complexity of certain constructive logics,” Mathematical Notes, (1993): 701–709. Translated from Matematicheskie Zametki, 52 (1992): 94–104. (Scholar)
Plotkin, G. and Stirling, C., 1986, “A framework for intuitionistic modal logic,” in TARK ’86: Proceedings of the 1986 conference on theoretical aspects of reasoning about knowledge, J. Halpern (ed.), Morgan Kaufmann Publishers, Los Altos 1986: 399–406. Abstract in Journal of Symbolic Logic 53(2): 669.
Rasiowa, H., 1974, Algebraic Approach to Non-Classical Logics, Amsterdam: North-Holland. (Scholar)
Rasiowa, H. and Sikorski, R., 1963, The Mathematics of Metamathematics, Warsaw: Panstwowe Wydawnictwo Naukowe. (Scholar)
Rathjen, M., 2006, “Realizability for constructive Zermelo-Fraenkel set theory,” in Logic Colloquium 2003 (Lecture Notes in Logic 24), J. Väänänen et al. (eds.), A. K. Peters 2006: 282–314. (Scholar)
–––, 2012, “From the weak to the strong existence property,” Annals of Pure and Applied Logic, 163: 1400–1418. (Scholar)
Rose, G. F., 1953, “Propositional calculus and realizability,” Transactions of the American Mathematical Society, 75: 1–19. (Scholar)
Ruitenberg, W., 1991, “The unintended interpretations of intuitionistic logic”, in: T. Drucker (ed.), Perspectives on the History of Mathematical Logic, Birkhauser 1991: 134–160. (Scholar)
Rybakov, V., 1997, Admissibility of Logical Inference Rules, Amsterdam: Elsevier. (Scholar)
Scott, D., 1968, “Extending the topological interpretation to intuitionistic analysis,” Compositio Mathematica, 20: 194–210. (Scholar)
Shulman, M., 2022, “Affine logic for constructive mathematics”, Bulletin of Symbolic Logic, 28: 327–386. (Scholar)
Simpson, A. K., 1994, The proof theory and semantics of intuitionistic modal logic, Doctoral dissertation, University of Edinburgh. (Scholar)
Smorynski, C. A., 1973, “Applications of Kripke models,” in Troelstra (ed.) 1973: 324–391. (Scholar)
Spector, C., 1962, “Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics,” Recursive Function Theory: Proceedings of Symposia in Pure Mathematics, Volume 5, J. C. E. Dekker (ed.), Providence, RI: American Mathematical Society, 1–27. (Scholar)
van Stigt, W. P., 1990, Brouwer’s Intuitionism, Amsterdam: North-Holland. (Scholar)
Stone, M. H., 1937, “Topological representation of distributive lattices and Brouwerian logics”, Casopis Pest. Mat. Fys., 67: 1–25. (Scholar)
Swart, H. C. M. de, 1976, “Another intuitionistic completeness proof,” Journal of Symbolic Logic 41: 644–662. (Scholar)
Tarski, A., 1938, “Der Aussagenkalkül und die Topologie”, Fundamenta Mathematicae, 31: 103–134. (Scholar)
Tennant, N., 2017, Core Logic, Oxford University Press, Oxford. (Scholar)
Troelstra, A. S., 1977, Choice Sequences: A Chapter of Intuitionistic Mathematics, Oxford Logic Guides, Clarendon Press, Oxford. (Scholar)
–––, 1991, “History of constructivism in the twentieth century,” ITLI Prepublication Series ML–1991–05, Amsterdam. Final version in Set Theory, Arithmetic and Foundations of Mathematics (Lecture Notes in Logic 36), J. Kenney and R. Kossak (eds.), Association for Symbolic Logic, Ithaca, NY, 2011: 150–179. (Scholar)
–––, 1998, “Realizability,” Chapter VI of Buss (ed.), 1998: 407–473. (Scholar)
–––, Introductory note to 1958 and 1972, in Gödel, 1990: 217–241.
Troelstra, A. S. (ed.), 1973, Metamathematical Investigation of Intuitionistic Arithmetic and Analysis (Lecture Notes in Mathematics 344), Berlin: Springer-Verlag. Corrections and additions available from the editor. (Scholar)
Troelstra, A. S. and Schwichtenberg, H., 2000, Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science: Volume 43), 2nd edition, Cambridge: Cambridge University Press. (Scholar)
Troelstra, A. S. and van Dalen, D., 1988, Constructivism in Mathematics: An Introduction, 2 volumes, Amsterdam: North-Holland Publishing. [See also the Corrections, in Other Internet Resources.] (Scholar)
Troelstra, A. S. and van Dalen, D. (eds.), 1982, The L. E. J. Brouwer Centenary Symposium, Amsterdam: North-Holland Publishing. (Scholar)
Veldman, W., 1976, “An intuitionistic completeness theorem for intuitionistic predicate logic,” Journal of Symbolic Logic, 41: 159–166. (Scholar)
–––, 1990, “A survey of intuitionistic descriptive set theory,” in P. P. Petkov (ed.), Mathematical Logic, Proceedings of the Heyting Conference, New York and London: Plenum Press, 155–174.
–––, 2005, “Two simple sets that are not positively Borel,” Annals of Pure and Applied Logic, 135: 151–209. (Scholar)
–––, 2021, “Intuitionism: An inspiration?,” Jahresbericht der Deutscher Mathematiker-Vereinigung, 123: 221–284. (Scholar)
Vesley, R. E., 1972, “Choice sequences and Markov’s principle,” Compositio Mathematica, 24: 33–53. (Scholar)
–––, 1970, “A palatable substitute for Kripke’s Schema,” in A. Kino et al. (eds.) 1970: 197ff. (Scholar)
Visser, A., 1999, “Rules and arithmetics,” Notre Dame Journal of Formal Logic, 40: 116–140. (Scholar)
–––, 2002, “Substitutions of \(\Sigma^{0}_1\) sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic,” Annals of Pure and Applied Logic, 114: 227–271. (Scholar)
–––, 2006, “Predicate logics of constructive arithmetical theories,” Journal of Symbolic Logic, 72: 1311–1326. (Scholar)

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