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

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

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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)
  • Benecerraf, P. and Hilary Putnam (eds.), 1983, Philosophy of Mathematics: Selected Readings, 2nd Edition, Cambridge: Cambridge University Press. (Scholar)
  • Brouwer, L. E. J., 1907, “On the Foundations of Mathematics,” Thesis, Amsterdam; English translation in Heyting (ed.) 1975: 11–101. (Scholar)
  • Brouwer, L. E. J., 1908, “The Unreliability of the Logical Principles,” English translation in Heyting (ed.) 1975: 107–111. (Scholar)
  • Brouwer, L. E. J., 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)
  • Brouwer, L. E. J., 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)
  • Brouwer, L. E. J., 1927, “Intuitionistic reflections on formalism,” originally published in 1927, English translation in van Heijenoort (ed.) 1967: 490–492. (Scholar)
  • Brouwer, L. E. J., 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)
  • 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)
  • 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,” Mathematsche Zeitschrift, 39: 176–210, 405–431. (Scholar)
  • Ghilardi, S., 1999, “Unification in intuitionistic logic,” Journal of Symbolic Logic, 64: 859–880. (Scholar)
  • Gödel, K., 1932, “Zum intuitionistischen Aussagenkalkül,” Anzeiger der Akademie der Wissenschaftischen in Wien 69: 65–66. Reproduced and translated with an introductory note by A. S. Troelstra in Gödel 1986: 222–225. (Scholar)
  • Gödel, K., 1933e, “Zur intuitionistischen Arithmetik und Zahlentheorie,” Ergebnisse eines mathematischen Kolloquiums, 4: 34–38. (Scholar)
  • Gödel, K., 1933f, “Eine Interpretation des intuitionistischen Aussagenkalküls,” reproduced and translated with an introductory note by A. S. Troelstra in Gödel 1986: 296–304. (Scholar)
  • Gödel, K., 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)
  • Gödel, K., 1986, Collected Works, Vol. I, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
  • Gödel, K., 1990, Collected Works, Vol. II, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
  • Glivenko, V., 1929, “Sur qulques points de la logique de M. Brouwer,” Academie Royale de Belgique, Bulletins de la classe des sciences, 5 (15): 183–188. (Scholar)
  • Harrop R., 1960, “Concerning formulas of the types ABC, A → (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)
  • Heyting, A., 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)
  • Iemhoff, R., 2001, “On the admissible rules of intuitionistic propositional logic,” Journal of Symbolic Logic, 66: 281–294. (Scholar)
  • Iemhoff, R., 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)
  • 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)
  • Kleene, S. C., 1952, Introduction to Metamathematics, Princeton: Van Nostrand. (Scholar)
  • Kleene, S. C., 1962, “Disjunction and existence under implication in elementary intuitionistic formalisms,” Journal of Symbolic Logic, 27: 11–18. (Scholar)
  • Kleene, S. C., 1963, “An addendum,” Journal of Symbolic Logic, 28: 154–156. (Scholar)
  • Kleene, S. C., 1965, “Classical extensions of intuitionistic mathematics,” in Bar-Hillel (ed.) 1965: 31-44. (Scholar)
  • Kleene, S. C., 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., 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)
  • 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, “CT0 is stronger than CT0!,” Proceedings of the American Mathematical Society, 73: 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)
  • Moschovakis, J. R., 1971, “Can there be no nonrecursive functions?,” Journal of Symbolic Logic, 36: 309–315. (Scholar)
  • Moschovakis, J. R., 2003, “Classical and constructive hierarchies in extended intuitionistic analysis,” Journal of Symbolic Logic, 68: 1015–1043. (Scholar)
  • Moschovakis, J. R., 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)
  • 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)
  • van Oosten, J., 2002, “Realizability: a historical essay,” Mathematical Structures in Computer Science, 12: 239–263. (Scholar)
  • van Oosten, J., 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)
  • 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)
  • Rathjen, M., 2012, “From the weak to the strong existence property,” Annals of Pure and Appled Logic, 163: 1400–1418. (Scholar)
  • Rose, G. F., 1953, “Propositional calculus and realizability,” Transactions of the American Mathematical Society, 75: 1–19. (Scholar)
  • Rybakov, V., 1997, Admissibility of Logical Inference Rules, Amsterdam: Elsevier. (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)
  • 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., 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)
  • Troelstra, A. S., 1998, “Realizability,” Chapter VI of Buss (ed.), 1998: 407–473. (Scholar)
  • Troelstra, A. S., Introductory note to 1958 and 1972, in Gödel, 1990: 217–241.
  • Troelstra, A. S. and van Dalen, D., 1988, Constructivism in Mathematics: An Introduction, 2 volumes, Amsterdam: North-Holland Publishing. (Scholar)
  • Veldman, W., 1976, “An intuitionistic completeness theorem for intuitionistic predicate logic,” Journal of Symbolic Logic, 41: 159–166. (Scholar)
  • Veldman, W., 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.
  • Veldman, W., 2005, “Two simple sets that are not positively Borel,” Annals of Pure and Applied Logic, 135: 151–209. (Scholar)
  • Vesley, R. E., 1972, “Choice sequences and Markov's principle,” Compositio Mathematica, 24: 33–53. (Scholar)
  • Vesley, R. E., 1970, “A palatable alternative to 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)
  • Visser, A., 2002, “Substitutions of Σ01 sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic,” Annals of Pure and Applied Logic, 114: 227–271. (Scholar)
  • Visser, A., 2006, “Predicate logics of constructive arithmetical theories,” Journal of Symbolic Logic, 72: 1311–1326. (Scholar)

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