Abstract
Among the logics that deal with the familiar connectives and quantifiers two stand out as having a solid philosophical—mathematical justification. On the one hand there is classical logic with its ontological basis and on the other hand intuitionistic logic with its epistemic motivation. The case for other logics is considerably weaker; although one may consider intermediate logics with more or less plausible principles from certain viewpoints none of them is accompanied by a comparably compelling philosophy. For this reason we have mostly paid attention to pure intuitionistic theories.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aczel, P.: 1968, ‘Saturated intuitionistic theories’, in Schmidt, et al. [1968], pp. 1–11.
Barendregt, H. P.: 1981, The Lambda Calculus. Its Syntax and Semantics, North-Holland, Amsterdam.
Beeson, M.: 1979, ‘A theory of constructions and proofs’, Preprint No. 134. Dept. of Math. Utrecht University.
Beeson, M.: 1985, Foundations of Constructive Mathematics. Metamathematical Studies, Springer-Verlag, Berlin.
Brouwer, L. E. J.: 1907, Over de Grondslagen der Wiskunde, Thesis, Amsterdam. Translation ‘On the foundations of mathematics’, in Brouwer [1975], pp. 11–101. New edition in Brouwer [ 1981 ].
Brouwer, L. E. J.: 1908. J.: 1908, ‘De onbetrouwbaarheid der logische principes’, Tijdschrift voor wijsbegeerte 2, 152–158. Translation ‘The unreliability of the logical principles’ in [1975], pp. 107–111. Also in [ 1981 ].
Brouwer, L. E. J.: 1918, ‘Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. I’, Koninklijke Nederlandse Akademie van Weten-schappen Verhandelingen le Sectie 12, no. 5, 43 p. Also in Brouwer [ 1975 ], pp. 150 – 190.
Brouwer, L. E. J.: 1975, Collected Works, I, (A. Heyting) (ed.), North-Holland, Amsterdam.
Brouwer, L. E. J.: 1981, Over de Grondslagen der Wiskunde, Aangevuld met Ongepub-liceerde Fragmenten, Correspondence met D. J. Korteweg. Recensies door G. Mannoury, etc., D. van Dalen (ed.), Mathematisch Centrum, varia 1, Amsterdam.
Brouwer, L. E. J.: 1981a, Brouwer’s Cambridge Lectures on Intuitionism, D. van Dalen (ed.), Cambridge University Press, Cambridge.
Burgess, J. P.: 1981, The completeness of intuitionistic propositional calculus for its intended interpretation’, Notre Dame J. Formal Logic 22, 17 – 28.
Chang, C. C. and Keisler, H. J.: 1973, Model Theory, North-Holland, Amsterdam.
Curry, H. B. and Feys, R.: 1958, Combinatory Logic I, North-Holland, Amsterdam.
Van Dalen, D.: 1973, ‘Lectures on intuitionism’, in Mathias and Rogers [1973], pp. 1–94.
Van Dalen, D.: 1974, ‘A model for HAS. A topological interpretation of the theory of species of natural numbers’, Fund Math. 82, 167 – 174.
Van Dalen, D.: 1977, ‘The use of Kripke’s Schema as a reduction principle’, J. Symbolic Logic 42, 238 – 240.
Van Dalen, D.: 1978, ‘An interpretation of intuitionistic analysis’, Ann. Math. Logic 13, 1 – 43.
Van Dalen, D.: 1980, Logic and Structure, Springer-Verlag, Berlin.
Van Dalen, D.: 1984, D.: 1984, ‘How to glue analysis models’, J. Symbolic Logic 49, pp. 1339– 1349.
Van Dalen, D.: 198x, ‘Glueing of analysis models in an intuitionistic setting’. To appear.
Van Dalen, D. and Statman, R.: 1979, ‘Equality in the presence of apartness’, in Hintikka et al. [ 1979 ], pp. 95 – 118.
Davis, M. (ed.): 1965, The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Raven Press, New York.
Demuth, O. and KuSera, A.: 1979, ‘Remarks on constructive mathematical analysis’, in M. Boffa, D. van Dalen, and K. McAloon (eds.), Logic Colloquium ’78, North-Holland, Amsterdam, pp. 81 – 130.
Dummett, M.: 1973, ‘The philosophical basis of intuitionistic logic’, in H. E. Rose and J. C. Sheperdson (eds.), Logic Colloquium ’73, North-Holland, Amsterdam, pp. 5–40. Also in Dummett, M.: 1978, Truth and Other Enigmas, Duckworth, London, pp. 215 – 247.
Dummett, M.: 1977, Elements of Intuitionism, Oxford University Press, Oxford.
Dyson, V. H. and Kreisel, G.: 1961, Analysis of Beth’s Semantic Construction of Intuitionistic Logic, Technical Report no. 3. Appl. math, and statistics lab. Stanford University, 65 pp.
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.
Fenstad, J. E. (ed.): 1971, Proceedings of the Second Scandanavian Logic Symposium, North-Holland, Amsterdam.
Fine, K.: 1970, ‘An intermediate logic without the finite model property’ (unpublished).
Fitting, M. C.: 1969, Intuitionistic Logic, Model Theory and Forcing, North-Holland, Amsterdam.
Fourman, M.: 1982, ‘Notions of choice sequence’, in Troelstra and van Dalen [1982], pp.91–106.
Fourman, M. P. and Scott, D. S.: 1979, ‘Sheaves and logic’, in Fourman, Mulvey, Scott [ 1979 ],pp. 302 – 401.
Fourman, M. P., Mulvey, C. J., and Scott, D. S.: 1979, Applications of Sheaves. Proceedings Durham 1977, Lecture Notes No. 753, Springer-Verlag, Berlin.
Fraenkel, A., Bar-Hillel, Y., Levy, A., and van Dalen, D.: 1973, Foundations of Set Theory, North-Holland, Amsterdam.
Friedman, H.: 1975, ‘The disjunction property implies the numerical existence property’, Proc. Nat. Acad. Sci. 72, 2877 – 2878.
Friedman, H.: 1977, ‘The intuitionistic completeness of intuitionistic logic under Tarskian semantics’, Abstract, SUNY at Buffalo.
Friedman, H.: 1977a, ‘New and old results on completeness of HPC’, Abstract, SUNY at Buffalo.
Friedman, H.: 1977b, ‘Classically and intuitionistically provably recursive functions’, in Higher Set Theory, Springer-Verlag, Berlin, pp. 21 – 27.
Gabbay, D. M.: 1970, ‘Decidability of the Kreisel-Putnam system’, J. Symbolic Logic 35, 431 – 437.
Gabbay, D. M.: 1977, ‘On some new intuitionistic propositional connectives’, Studia Logica 36, 127 – 139.
Gabbay, D. M.: 1981, Semantical Investigations in Hey ting’s Intuitionistic Logic, D. Reidel, Dordrecht.
Gabbay, D. M. and De Jongh, D. H.: 1974, ‘Sequences of decidable finitely axiomatizable intermediate logics with the disjunction property’, J. Symbolic Logic 39, 67 – 79.
Gentzen, G.: 1933, ‘Über das Verhaltnis zwischen intuitionistischer und klassischer Arithmetik’, English translation in Szabo [1969], pp. 53 – 67.
Girard, J. Y.: 1971, ‘Une extension de l’interpretation de Gödel a l’analyse et son application à l’élimination des coupures dans l’analyse et la théorie des types’, in Fenstad [ 1971 ] pp. 63 – 92.
Glivenko, V.: 1929, ‘Sur quelques points de la logique de M. Brouwer’, Academie Royale de Belgique, Bull, de la class des sciences (5), Vol. 15, pp. 183–188.
Goad, C. A.: 1978, ‘Monadic infinitary propositional logic: a special operator’, Repts Math. Logic 10, 43–50.
Gödel, K.: 1932, Zum intuitionistischen AussagenkalkuF, Akademie der Wissenschaften in Wien. Math. - naturwiss. Klctsse. Anzeiger 69, 65–66. Also in Ergebnisse eines Math. Koll. 4, 42.
Gödel, K.: 1933, ‘Zur intuitionistischen Arithmetik und Zahlentheorie’, Ergebnisse eines mathematischen Kolloqiums 4, 34–38. English translation in [Davis, 1965], pp. 75–81. Cf. J. Symbolic Logic 31(1966) 484 – 494.
Gödel, K.: 1958, ‘Über eine bisher noch nicht beniitzte Erweiterung des finiten Stand-punktes’, Dialectica 12, 280–287. English translation in J. Philosophical Logic 9(1980) 133 – 142.
Goldblatt, R.: 1979, Topoi. The Categorical Analysis of Logic, North-Holland, Amsterdam (revised edition, 1984 ).
Gornemann, S.: 1971, A logic strong than intuitionism’, J. Symbolic Logic 36, 249 – 261.
Grayson, R.: 1981, ‘Concepts of general topology in constructive mathematics and in sheaves’, Ann. Math. Logic 20, 1 – 41.
Grayson, R.: 1984, ‘Heyting-valued semantics’, in G. Lolli, G. Longo, and A. Marcja (eds.), Logic Colloqium ’82, North-Holland, Amsterdam, pp. 181 – 208.
Grzegorczyk, A.: 1964, ‘A philosophically plausible interpretation of intuitionistic logic’, Indagationes Mathematicae 26, 569 – 601.
Harrop, R.: 1958, ‘On the existence of finite models and decision procedures for propositional calculi’,Proc. Camb. Phil. Soc. 54,1–13.
Hartog, W. den: 1978, ‘A Proof Theoretic Study. The Theory of Pseudo-Order as a Conservative Extension of the Theory of Apartness’, Dept. of Math. Rijksuniversi-teit Utrecht, Preprint no. 77.
Heijenoort, J. van: 1967, From Frege to Gödel, A scource book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge Mass.
Heyting, A.: 1930, A.: 1930, ‘Die formalen Regeln der intuitionistischen Logik’, Sitzungsberichte der preussischen Akademie von Wissenschaften, pp. 42–56. ‘Die formalen Regeln der intuitionistischen Mathematik’, Ibid. pp. 57–71, 158–169. Also (partly) in Two Decades of Mathematics in the Netherlands, Amsterdam, 1978.
Heyting, A.: 1956, Intuitionism. An Introduction, North-Holland, Amsterdam.
Hintikka, J., Niiniluoto, I., and Saarinen, E. (eds.): 1979, Essays on Mathematical and Philosophical Logic, D. Reidel, Dordrecht.
Hoeven, G. van der and Moerdijk, I.: 1984, ‘Sheaf models for choice sequences’, Annals of Pure and Applied Logic 27, 63 – 107.
Hosoi, T.: 1967, ‘On intermediate logics, I’, J. Fac. Sci. Univ. of Tokyo 14, 293 – 312.
Howard, W.: 1980, ‘The formulae-as-types notion of construction’, in Seldin and Hindley [1980], pp. 479–490.
Hughes, G. E. and Cresswell, M. J.: 1968, An Introduction to Modal Logic, Methuen, London.
Hull, R. C.: 1969, ‘Counterexamples in intuitionistic analysis using Kripke’s schema’, Z. Math. Logik und Grundlagen der Math. 15, 241 – 246.
Hyland, M.: 1982, ‘The effective topos’, in Troelstra and van Dalen [1982] pp. 165–216.
Hyland, M., Johnstone, P. T. and Pitts, A. M.: 1980, ‘Tripos theory’, Math. Proc. Cambr. Phil. Soc. 88, 205 – 232.
Jankov, V. A.: 1968, ‘Constructing a sequence of strongly independent super-intuitionistic propositional calculi’, Soviet Math. Dok 9, 806 – 807.
Jaskowski, S.: 1936, ‘Recherches sur le systeme de la logique intuitioniste’, Actes du Congrés Intern, de Phil. Scientifique. VI. Phil des mathématiques, Act. Sc. et Ind 393, Paris, pp. 58–61.
Johansson, I.: 1936, ‘Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus’, Compositio Math. 4, 119 – 136.
Jongh, D. H. de: 1980, ‘A class of intuitionistic connections’, in J. Barwise, H. J. Keisler and K. Kunen (eds.), The Kleene Symposium, North-Holland, Amsterdam, pp. 103 – 112.
Jongh, D. H. de and Smoryński, C.: 1976, ‘Kripke models and the intuitionistic theory of species’, Ann. Math. Logic 9, 157 – 186.
Kino, A., Myhill, J. and Vesley, R. E.: 1970, Intuitionism and Proof Theory. Proceedings of the Summer Conference at Buffalo, New York, 1968, North-Holland, Amsterdam.
Kleene, S. C.: 1952, Introduction to Meta-mathematics, North-Holland, Amsterdam.
Kleene, S. C.: 1973, ‘Readability: A retrospective survey’, in Mathias and Rogers [ 1973 ],pp. 95 – 112.
Kleene, S. C. and Vesley, R. E.: 1965, The Foundations of Intuitionistic Mathematics, Especially in Relation to Recursive Functions, North-Holland, Amsterdam.
Klop, J. W.: 1980, Combinatory Reduction Systems, Thesis, Rijks Universiteit Utrecht. Also MC Tract 127. Math. Centre Amsterdam.
Kolmogorov, A. N.: 1925, ‘On the principle of the excluded middle’ (Russian), Matematičeski Sbornik 32, 646–667. English translation in Van Heijenoort [ 1967 ], pp. 414 – 437.
Kreisel, G.: 1958, ‘A remark on free choice sequences and the topological completeness proofs’, J. Symbolic Logic 23, 369 – 388.
Kreisel, G.: 1959, ‘Interpretations of analysis by means of constructive functional of finite type’, in A. Heyting (ed.), Constructivity in Mathematics, North-Holland, Amsterdam, pp. 101 – 128.
Kreisel, G.: 1965, ‘Mathematical logic’, in T. L. Saaty (ed.), Lectures on Modern Mathematics III, Wiley & Sons, New York, pp. 95 – 195.
Kreisel, G.: 1967, ‘Informal rigour and completeness proofs’, in I. Lakatos (ed.), Problems in the Philosophy of Mathematics, North-Holland, Amsterdam.
Kreisel, G.: 1970, ‘Church’s Thesis, a kind of reducibility axiom of constructive mathematics’, in Kino et al. [1970], pp. 121–150.
Kreisel, G. and Putnam, H.: 1957, ‘Eine Unableitbarkeitsbeweismethode fur den intuitionistischen Aussagenkalkul’, Archiv. f. math. Logik 3, 74 – 78.
Kreisel, G. and Troelstra, A. S.: 1970, ‘Formal systems for some branches of intuitionistic analysis’, Ann. Math. Logic 1, 229 – 387.
Kripke, S.: 1963, ‘Semantical analysis of intuitionistic logic I’, in J. Crossley and M. Dummett (eds.), Formal Systems and Recursive Functions, North-Holland, Amsterdam, pp. 92 – 129.
Leivant, D.: 1976, ‘Failure of completeness properties of intuitionistic predicate logic for constructive models’, Ann. Sc. Univ. Clermont. Ser Math. 13, 93 – 107.
Leivant, D.: 198x, ‘Syntactic translations and provably recursive functions’. To appear in the J. Symbolic Logic.
Leivant, D.: 198y, ‘Intuitionistic formal systems’. To appear.
Lemmon, E., and Scott, D. S.: 1966, ‘Intensional logics’, published in 1977 as An Introduction to Modal Logic, K. Segerberg (ed.), Blackwell, Oxford.
Lifshits, V. A.: 1969, ‘Problems of decidability for some constructive theories of equalities’, in A. O. Slisenko (ed.), Studies in Constructive Mathematics and Mathematical Logic, ( Consultants Bureau, New York.
Markov, A. A.: 1950, ‘Konstruktivnaja logika’, Usp. Mat. Nauk 5, 187 – 188.
Martin-Lof, P.: 1977, ‘Hauptsatz for the theory of species’, in Fenstad [1971 ].
Martin-Lof, P.: 1982, ‘Constructive mathematics and computer programming’, in L. J. Cohen, J. Los, H. Pfeiffer and K. P. Podewski (eds.), Logic, Methodology and Philosophy of Science VI, North-Holland, Amsterdam, pp. 153 – 179.
Martin-Lof, P.: 1984, Intuitionistic Type Theory, Notes by G. Sambin of a series of lectures given in Padova, June 1982. Bibliopolis, Naples.
Mathias, A. R. D. and Rogers, H. Jr.: 1973, Cambridge Summer School in Mathematical Logic, Springer Lecture Notes No. 337, Berlin.
Maximova, L. L.: 1977, ‘Craig interpolation theorem and amalgamable varieties’, Soviet Math. Dok. 18, 1550 – 1553.
Mine, G.: 1966, ‘Skolem’s method of elimination of positive quantifiers in sequential calculi’, Dokl. Akad. Nauk SSSR169, 861 – 864.
Mine, G.: 1974, ‘On E-theorems’ (Russian), Investigation in constructive mathematics VI Zapisky Nauk. Sem. Leningrad Steklov Inst. 40,110–118.
Moschovakis, J.: 1967, ‘Disjunction and existence in formalized intuitionistic analysis’, In J. N. Crossley (ed.), Sets, Models and Recursion Theory, North-Holland, Amsterdam, 309 – 331.
Moschovakis, J.: 1973, ‘A topological interpretation of second-order intuitionistic arithmetic’, Comp. Math. 26, 261 – 276.
Moschovakis, J.: 1980, ‘A disjunctive decomposition theorem for classical theories’, in F. Richman (ed.), Constructive Mathematics, Springer Verlag, Berlin, pp. 250 – 259.
Nelson, D.: 1949, ‘Constructive falsity’, J. Symbolic Logic 14, 16 – 26.
Nishimura, T.: 1966, ‘On formulas of one variable in intuitionistic propositional calculus’, J. Symbolic Logic 25, 327 – 331.
Ono, H.: 1972, ‘Some results on intermediate logics’, Publ. RIMS, Kyoto University8, 117 – 130.
Ono, H.: 1973, ‘A study of intermediate predicate logics’, Publ. RIMS Kyoto University8, 619 – 649.
Ono, H.: 198x, ‘Semantical analysis of predicate logics without the contraction rule’ (to appear in Studia Logica).
Ono, H. and Komori, Y.: 198x, ‘Logics without the contraction rule’ (to appear in the J. Symbolic Logic).
Posy, C. J.: 1976, ‘Varieties of indeterminacy in the theory of general choice sequences’, J.Phil. Logic 5, 91 – 132.
Posy, C. J.: 1977, ‘The theory of empirical sequences’, J. Philosophical Logic 6, 47 – 81.
Posy, C. J.: 1980, ‘On Brouwer’s definition of unextendable order’, History and Phil. Logic 1, 139 – 149.
Pottinger, G.: 1976, ‘A new way of normalizing intuitionist propositional logic’, Studia Logica 35, 387 – 408.
Prawitz, D.: 1965, Natural Deduction. A Proof Theoretical Study, Almqvist & Wiksell, Stockholm.
Prawitz, D.: 1970, ‘Some results for intuitionistic logic with second-order quantification rules’, in Kino, Myhill, and Vesley [ 1970 ], pp. 259 – 270.
Prawitz, D.: 1971, ‘Ideas and results in proof theory’, in J. E. Fenstad [1971 ].
Prawitz, D.: 1977, ‘Meanings and proofs: on the conflict between classical and intuitionistic logic’, Theoria 43, 2 – 40.
Prawitz, D.: 1979, ‘Proofs and the meaning and the completeness of the logical constants’, in Hintikka et al. [1979], pp. 25–40.
Prawitz, D and Malmnés, P.: 1968, ‘A survey of some connections between classical, intuitionistic and minimal logic’, in H. A. Schmidt et al., pp. 215–229.
Rasiowa, H.: 1974, An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam.
Rasiowa, H. and Sikorski, R.: 1963, The Mathematics of Metamathematics, Panstwowe Wydawnictwo Naukowe Warszawa.
Rauszer, C.: 1980, ‘An algebraic and Kripke-style approach to a certain extension of intuitionistic logic’, Dissertationes Mathematicae CLXVII, Warszawa, 67 pp.
Rautenberg, W.: 1979, Klassische und nichtklassische Aussagenlogik, Vieweg & Sohn, Braunschweig/Wiesbaden.
Renardel de Lavalette, G. R.: 1981, ‘The interpolation theorem in fragments of logic’, Indag. Math. 43, 71 – 86.
Schmidt, H. A., Schutte, K., and Thiele, H. J. (eds.): 1968, Contributions to Mathematical Logic, North-Holland, Amsterdam.
Schiitte,K.: 1968, Vollständige Systeme modaler und intuitionistischer Logik, Ergebnisse der Mathematik und ihrer Grenzgebiete, 42, Springer-Verlag, Berlin.
Scott, D. S.: 1968, ‘Extending the topological interpretation to intuitionistic analysis’, Comp. Math. 20, 194 – 210.
Scott, D. S.: 1970, ‘Extending the topological interpretation to intuitionistic analysis II’, in Kino, Myhill, and Vesley [ 1970 ], pp. 235 – 255.
Scott, D. S.: ‘Identity and existence in intuitionistic logic’, in Fourman, Mulvey, and Scott[1979], pp.660–696.
Segerberg, K.: 1968, ‘Propositional logics related to Heyting’s and Johansson’s’, Theoria 34, 26 – 61.
Seldin, J. P. and Hindley, J. R. (eds.): 1980, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, London.
Shoenfield, J. R.: 1967, Mathematical Logic, Addison-Wesley, Reading, Mass.
Smorynski, C.: 1973, ‘Investigation of Intuitionistic Formal Systems by Means of Kripke Models’, Diss. Univ. of Illinois.
Smorynski, C.: 1973a, ‘Elementary intuitionistic theories’, J. Symbolic Logic 38, 102 – 134.
Smorynski, C.: 1977, ‘On axiomatizing fragments’, J. Symbolic Logic 42, 530 – 544.
Smorynski, C.: 1978, ‘The axiomatization problem for fragments’, Ann. Math. Logic 14, 193 – 221.
Smorynski, C.: 1982, ‘Non-standard models and constructivity’, in Troelstra and van Dalen [1982], 459–464.
Stein, M.: 1980, ‘Interpretations of Heyting’s Arithmetic. An analysis by means of a language with set symbols’, Ann. Math. Logic 19, 1 – 31.
Sundholm, G.: 1983, ‘Constructions, proofs and the meanings of the logical constants’, J. Phil. Logic 12, 151 – 172.
Swart, H. C. M. de: 1976, ‘Another intuitionistic completeness proof’, J. Symbolic Logic 41, 644 – 662.
Szabo, M. E. (ed.): 1969, The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam.
Tait, N.: 1975, ‘A readability interpretation of the theory of species’, in R. Parik (ed.), Logic Colloquium, Springer-Verlag, Berlin, 240 – 251.
Takahashi, M.: 1970, ‘Cut-elimination theorem and Brouwerian-valued models for intuitionistic type theory’, Comment. Math. Univ. St. Pauli 19, 55 – 72.
Thomason, R. H.: 1969, ‘A semantical study of constructible falsity’, Z. Math. Logik und Grundlagen der Mathematik 15, 247 – 257.
Troelstra, A. S.: 1969, Principles of Intuitionism, Springer-Verlag, Berlin.
Troelstra, A. S.: 1973, Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Springer-Verlag, Berlin.
Troelstra, A. S.: 1973a, ‘Notes on intuitionistic second-order arithmetic’, in Mathias and Rogers [ 19 7 3 ], pp. 171–205.
Troelstra, A. S.: 1977, Choice Sequences. A Chapter of Intuitionistic Mathematics, Oxford University Press, Oxford.
Troelstra, A. S.: 1978, ‘Commentary on Heyting [1930]’, in Two Decades of Mathematics in the Netherlands, Part 5, Math. Centre, Amsterdam.
Troelstra, A. S.: 1979, A supplement to ‘Choice Sequences’, Report 79–04 of the Math. Institute University of Amsterdam. 22 pp.
Troelstra, A. S.: 1980, ‘The interplay between logic and mathematics: intuitionism’, in E. Agazzai (ed.),Modem Logic - A Survey, D. Reidel, Dordrecht, pp. 197 – 221.
Troelstra, A. S.: 1981, ‘On a second-order propositional operator in intuitionistic logic’, Studia Logica 40, 113 – 140.
Troelstra, A. S.: 1981a, ‘Arend Heyting and his contribution to Intuitionism’, Nieuw Archief voor Wiskunde 24, pp. 1 – 23.
Troelstra, A. S.: 1983, ‘Analyzing choice sequences’, J. Philosophical Logic 12, 197 – 260.
Troelstra, A. S. and Van Dalen, D. (eds.): 1982, The L. E. J. Brouwer Centenary Symposium, North-Holland, Amsterdam.
Troelstra, A. S. and Van Dalen, D.: 198x, Constructivism in Mathematics, To appear.
Veldman, W.: 1976, ‘An intuitionistic completeness theorem for intuitionistic predicate logic’, J. Symbolic Logic 41, 159 – 166.
Visser, A. ‘On the Completeness Principle: a study of provability in Heyting’s Arithmeticá, 1982, Annals Math. Logic 22, 263–295.
Zucker, J. T. and Tragesser, R. S.: 1978, ‘The adequacy problem for inferential logic’, J. Philosophical Logic 7, 501–516.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Van Dalen, D. (1986). Intuitionistic Logic. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Synthese Library, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5203-4_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-5203-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8801-5
Online ISBN: 978-94-009-5203-4
eBook Packages: Springer Book Archive