Linked bibliography for the SEP article "Constructive Mathematics" by Douglas Bridges, Erik Palmgren and Hajime Ishihara

This is an automatically generated and experimental page

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.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

References

  • Aberth, O., 1980, Computable Analysis, New York: McGraw-Hill. (Scholar)
  • –––, 2001,Computable Calculus, New York: Academic Press. (Scholar)
  • Bauer, A., 2005, “Realizability as the connection between computable and constructive Mathematics”, Lecture notes for a tutorial at a satellite seminar of CCA2005, Kyoto, Japan [available online]. (Scholar)
  • Beeson, M., 1985, Foundations of Constructive Mathematics, Heidelberg: Springer Verlag. (Scholar)
  • Berger, J., 2006, “The logical strength of the uniform continuity theorem”, in Logical Approaches to Computational Barriers, A. Beckmann, U. Berger, B. Löwe, and J. V. Tucker (eds.), Heidelberg: Springer Verlag. (Scholar)
  • Berger, J., and Bridges, D.S., 2007, “A fan-theoretic equivalent of the antithesis of Specker’s theorem”, Proceedings of Royal Dutch Mathematical Society (Indagationes Mathematicae) (Indag. Math. N.S.), 18(2): 195–202. (Scholar)
  • –––, 2009, “The fan theorem and positive-valued uniformly continuous functions on compact intervals”, New Zealand Journal of Mathematics, 38: 129–135. (Scholar)
  • Berger, J., and Ishihara, H., 2005, “Brouwer’s fan theorem and unique existence in constructive analysis”, Mathematical Logic Quarterly, 51(4): 360–364. (Scholar)
  • Berger, J., and Schuster, P.M., 2006, “Classifying Dini’s theorem”, Notre Dame Journal of Formal Logic, 47: 253–262. (Scholar)
  • Berger, J., and Svindland, G., 2016, “A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov’s principle ”, Annals of Pure and Applied Logic, 167: 1161–1170. (Scholar)
  • –––, 2016a, “Convexity and constructive infima”, Archive for Mathematical Logic, 55: 873–881. (Scholar)
  • Bishop, E., 1967, Foundations of Constructive Analysis, New York: McGraw-Hill. (Scholar)
  • –––, 1973, Schizophrenia in Contemporary Mathematics (American Mathematical Society Colloquium Lectures), Missoula: University of Montana; reprinted in Errett Bishop: Reflections on Him and His Research, American Mathematical Society Memoirs 39. (Scholar)
  • Bishop, E. and Bridges, D., 1985, Constructive Analysis, (Grundlehren der mathematischen Wissenschaften, 279), Heidelberg: Springer Verlag. (Scholar)
  • Bourbaki, N., 1984, Éléments d’histoire des mathématiques, Paris: Masson; English-language edition, Elements of the History of Mathematics, J. Meldrum (trans.), 2006, Berlin: Springer Verlag.
  • Bridges, D.S., 1999, “Constructive methods in mathematical economics”, in Zeitschrift für Nationalökonomie (Supplement), 8: 1–21. (Scholar)
  • Bridges, D.S., and Diener, H., 2007, “The pseudocompactness of [0, 1] is equivalent to the uniform continuity theorem”, Journal of Symbolic Logic, 72(4): 1379–1383. (Scholar)
  • Bridges, D.S., and Richman, F., 1987, Varieties of Constructive Mathematics, London Mathematical Society Lecture Notes 97, Cambridge: Cambridge University Press. (Scholar)
  • Bridges, D.S. and Vîță, L.S., 2006, Techniques of Constructive Analysis, Heidelberg: Springer Verlag. (Scholar)
  • –––, 2011, Apartness and Uniformity—A Constructive Development, Heidelberg: Springer Verlag. (Scholar)
  • Bridges, D.S., Ishihara, H., Rathjen, M.J., and Schwichtenberg, H. (eds), forthcoming, Handbook of Constructive Mathematics, Cambridge: Cambridge University Press. (Scholar)
  • Brouwer, L.E.J., 1907, Over de Grondslagen der Wiskunde, Doctoral Thesis, University of Amsterdam; reprinted with additional material, D. van Dalen (ed.), by Matematisch Centrum, Amsterdam, 1981. (Scholar)
  • –––, 1908, “De onbetrouwbaarheid der logische principes”, Tijdschrift voor Wijsbegeerte, 2: 152–158. (Scholar)
  • –––, 1921, “Besitzt jede reelle Zahl eine Dezimalbruchentwicklung?”, Mathematische Annalen, 83: 201–210. (Scholar)
  • –––, 1924, “Beweis, dass jede volle Funktion gleichmässig stetig ist”, Proceedings of Royal Dutch Mathematical Society, 27: 189–193. (Scholar)
  • –––, 1924A, “Bemerkung zum Beweise der gleichmässigen Stetigkeit voller Funktionen”, Proceedings of Royal Dutch Mathematical Society, 27: 644–646. (Scholar)
  • Cederquist, J., and Negri, S., 1996, “A constructive proof of the Heine-Borel covering theorem for formal reals”, in Types for Proofs and Programs (Lecture Notes in Computer Science, Volume 1158), 62–75, Berlin: Springer Verlag. (Scholar)
  • Constable, R., et al., 1986, Implementing Mathematics with the Nuprl Proof Development System, Englewood Cliffs, NJ: Prentice-Hall. (Scholar)
  • Coquand, T., 1992, “An intuitionistic proof of Tychonoff’s theorem”, Journal of Symbolic Logic, 57: 28–32. (Scholar)
  • –––, 2009, “Space of valuations”, Annals of Pure and Applied Logic, 157: 97–109. (Scholar)
  • –––, 2016, “Type Theory”, Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/entries/type-theory/>. (Scholar)
  • Coquand, T., and Spitters, B., 2009, “Integrals and Valuations”, Journal of Logic and Analysis, 1(3): 1–22. (Scholar)
  • Coquand, T., Sambin, G., Smith, J., and Valentini, S., 2003, “Inductively generated formal topologies”, Annals of Pure and Applied Logic, 124: 71–106. (Scholar)
  • Curi, G., 2010, “On the existence of Stone-Čech compactification”, Journal of Symbolic Logic, 75: 1137–1146. (Scholar)
  • Dent, J.E., 2013, Anti-Specker Properties in Constructive Reverse Mathematics, Ph.D. thesis, University of Canterbury, Christchurch, New Zealand. (Scholar)
  • Diaconescu, R., 1975, “Axiom of choice and complementation”, Proceedings of the American Mathematical Society, 51: 176–178. (Scholar)
  • Diener, H., 2008, Compactness under Constructive Scrutiny, Ph.D. thesis, Christchurch, New Zealand: University of Canterbury. (Scholar)
  • –––, 2008a, “Generalising compactness”, Mathematical Logic Quarterly, 51(1): 49–57. (Scholar)
  • –––, 2012,“Reclassifying the antithesis of Specker’s theorem”, Archive for Mathematical Logic, 51: 687–693. (Scholar)
  • Diener, H., and Loeb, I., 2009, “Sequences of Real Functions on [0, 1] in Constructive Reverse Mathematics”, Annals of Pure and Applied Logic, 157(1): 50–61. (Scholar)
  • Diener, H., and Lubarsky, R., 2013, “Separating the fan theorem and its weakenings”, in Logical Foundations of Computer Science (Lecture Notes in Computer Science, 7734), S. Artemov and A. Nerode (eds.), Berlin: Springer Verlag. (Scholar)
  • Dummett, Michael, 1977 [2000], Elements of Intuitionism (Oxford Logic Guides, 39), Oxford: Clarendon Press, 1977; 2nd edition, 2000. [Page references are to the 2nd edition.] (Scholar)
  • Ewald, W., 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics (Volume 2), Oxford: Clarendon Press. (Scholar)
  • Feferman, S, 1975, “A language and axioms for explicit mathematics”, in Algebra and Logit, J. N. Crossley (ed.), Heidelberg: Springer Verlag, pp. 87–139.
  • –––, 1979, “Constructive theories of functions and classes”, in Logic Colloquium ‘78, M. Boffa, D. van Dalen, and K. McAloon (eds.), Amsterdam: North Holland, pp. 159–224. (Scholar)
  • Friedman, H., 1975, “Some systems of second order arithmetic and their use”, in Proceedings of the 17th International Congress of Mathematicians, Vancouver, BC, 1974. (Scholar)
  • –––, 1977, “Set theoretic foundations for constructive analysis”, Annals of Mathematics, 105 (1): 1–28. (Scholar)
  • Goodman, N.D., and Myhill, J., 1978, “Choice Implies Excluded Middle”, Zeitschrift für Logik und Grundlagen der Mathematik, 24: 461. (Scholar)
  • Hayashi, S., and Nakano, H., 1988, PX: A Computational Logic, Cambridge MA: MIT Press. (Scholar)
  • Hendtlass, M., 2013, Constructing fixed points and economic equilibria, Ph.D. thesis, University of Leeds. (Scholar)
  • Heyting, A., 1930, “Die formalen Regeln der intuitionistischen Logik”, Sitzungsberichte der Preussische Akadademie der Wissenschaften. Berlin, 42–56. (Scholar)
  • –––, 1971, Intuitionism—an Introduction, 3rd edition, Amsterdam: North Holland. (Scholar)
  • Hilbert, D., 1925, “Über das Unendliche”, Mathematische Annalen, 95: 161–190; translation, “On the Infinite”, by E. Putnam and G. Massey, in Philosophy of Mathematics: Selected Readings, P. Benacerraf and H. Putnam (eds.), Englewood Cliffs, NJ: Prentice Hall, 1964, 134–151. (Scholar)
  • Hurewicz, W., 1958, Lectures on Ordinary Differential Equations, Cambridge, MA: MIT Press. (Scholar)
  • Ishihara, H., 1992, “Continuity properties in constructive mathematics”, Journal of Symbolic Logic, 57 (2): 557–565. (Scholar)
  • –––, 1994, “A constructive version of Banach’s inverse mapping theorem”, New Zealand Journal of Mathematics, 23: 71–75. (Scholar)
  • –––, 2005, “Constructive Reverse mathematics: compactness properties”, in From Sets and Types to Analysis and Topology: Towards Practicable Foundations for Constructive Mathematics, L. Crosilla and P. Schuster (eds.), Oxford: The Clarendon Press. (Scholar)
  • –––, 2006, “Reverse mathematics in Bishop’s constructive mathematics”, Philosophia Scientiae (Cahier Special), 6: 43–59. (Scholar)
  • –––, 2013, “Relating Bishop’s function spaces to neighbourhood spaces”, Annals of Pure and Applied Logic, 164: 482–490. (Scholar)
  • Johnstone, P.T., 1982, Stone Spaces, Cambridge: Cambridge University Press. (Scholar)
  • –––, 2003, “The point of pointless topology”, Bulletin of the American Mathematical Society, 8: 41–53. (Scholar)
  • Joyal, A., and Tierney, M., 1984, “An extension of the Galois theory of Grothendieck”, Memoirs of the American Mathematical Society, 309: 85 pp. (Scholar)
  • Julian, W.H., and Richman, F., 1984, “A uniformly continuous function on [0, 1] that is everywhere different from its infimum”, Pacific Journal of Mathematics, 111: 333–340.
  • Kushner, B., 1985, Lectures on Constructive Mathematical Analysis, Providence, RI: American Mathematical Society. (Scholar)
  • Lietz, P., 2004, From Constructive Mathematics to Computable Analysis via the Realizability Interpretation, Dr. rer. nat. dissertation, Universität Darmstadt, Germany. (Scholar)
  • Lietz, P., and Streicher, T., “Realizability models refuting Ishihara’s boundedness principle”, Annals of Pure and Applied Logic, 163(12): 1803–1807. (Scholar)
  • Loeb, I., 2005, “Equivalents of the (Weak) Fan Theorem”, Annals of Pure and Applied Logic, 132: 51–66. (Scholar)
  • Lombardi, H., Quitté, C., 2011, Algèbre Commutative. Méthodes constructives, Nanterre, France: Calvage et Mounet. (Scholar)
  • Lorenzen, P., 1955, Einführung in die operative Logik und Mathematik (Grundlehren der mathematischen Wissenschaften, Volume 78), 2nd edition, 1969, Heidelberg: Springer. (Scholar)
  • Lubarsky, R., and Diener, H., 2014, “Separating the Fan Theorem and Its Weakenings”, Journal of Symbolic Logic, 79(3): 792–813. (Scholar)
  • Markov, A.A., 1954, Theory of Algorithms, Trudy Mat. Istituta imeni V.A. Steklova, 42, Moskva: Izdatel’stvo Akademii Nauk SSSR. (Scholar)
  • Marquis, J.-P., “Category Theory”, 2015, The Stanford Encyclopedia of Philosophy (Winter 2015 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2015/entries/category-theory/>. (Scholar)
  • Martin-Löf, P., 1968, Notes on Constructive Analysis, Stockholm: Almquist & Wiksell. (Scholar)
  • –––, 1975, “An intuitionistic theory of types: predicative part”, in Logic Colloquium 1973, H.E. Rose and J.C. Shepherdson (eds.), Amsterdam: North-Holland. (Scholar)
  • –––, 1980, “Constructive mathematics and computer programming”, in Proc. 6th. Int. Congress for Logic, Methodology and Philosophy of Science, L. Jonathan Cohen (ed.), Amsterdam: North-Holland. (Scholar)
  • –––, 1984, Intuitionistic Type Theory, Notes by Giovanni Sambin of a series of lectures given in Padova, June 1980, Naples: Bibliopolis. (Scholar)
  • –––, 2006, “100 years of Zermelo’s axiom of choice: what was the problem with it?”, The Computer Journal, 49(3): 345–350. (Scholar)
  • Menger, K., 1940, “Topology without points”, Rice Institute Pamphlet, 27(1): 80–107 [available online]. (Scholar)
  • Mines, R., Richman, F., and Ruitenburg, W., 1988, A Course in Constructive Algebra, Universitext, Heidelberg: Springer Verlag. (Scholar)
  • Moerdijk, I., 1984, “Heine-Borel does not imply the fan theorem”, Journal of Symbolic Logic, 49(2): 514–519. (Scholar)
  • Moore, G.H., 2013, Zermelo’s Axiom of Choice: Its Origins, Development, and Influence, New York: Dover. (Scholar)
  • Myhill, J., 1973, “Some Properties of Intuitionistic Zermelo-Fraenkel Set Theory”, in Cambridge Summer School in Mathematical Logic, A. Mathias and H. Rogers (eds.), Lecture Notes in Mathematics, 337, Heidelberg: Springer Verlag, 206–231. (Scholar)
  • –––, 1975, “Constructive Set Theory”, Journal of Symbolic Logic, 40(3): 347–382. (Scholar)
  • Naimpally, S., 2009, Proximity Approach to Problems in Topology and Analysis, Munich: Oldenbourg Verlag. (Scholar)
  • Naimpally, S., and Warrack, B.D., 1970, Proximity Spaces (Cambridge Tracts in Math. and Math. Phys., Volume 59), Cambridge: Cambridge University Press. (Scholar)
  • Nordström, B., Peterson, K., and Smith, J.M., 1990, “Programming in Martin-Löf’s Type Theory”, Oxford: Oxford University Press. (Scholar)
  • Palmgren, E., 2007, “A constructive and functorial embedding of locally compact metric spaces into locales”, Topology and its Applications, 154: 1854–1880.
  • –––, 2008, “Resolution of the uniform lower bound problem in constructive analysis”, Mathematical Logic Quarterly, 54: 65–69. (Scholar)
  • –––, 2009, “From intuitionistic to formal topology: some remarks on the foundations of homotopy theory”, in: Logicism, Intuitionism and Formalism—what has become of them?, S. Lindström, E. Palmgren, K. Segerberg, and V. Stoltenberg-Hansen (eds.), 237–253, Berlin: Springer Verlag. (Scholar)
  • Petrakis, I., 2016, “A constructive function-theoretic approach to topological compactness”, in Logical Methods in Computer Science 2016, IEEE Computer Society Publications: 605–614.
  • –––, 2016a, “The Urysohn Extension Theorem for Bishop Spaces”, in S. Artemov and A. Nerode (eds.), Symposium on Logical Foundations in Computer Science 2016 (Lecture Notes in Computer Science 9537), Berlin: Springer Verlag, 299–316. (Scholar)
  • Picado, J., and Pultr, A., 2011, Frames and Locales: Topology without Points, Basel: Birkhäuser Verlag. (Scholar)
  • Richman, F., 1983, “Church’s Thesis Without Tears”, Journal of Symbolic Logic, 48: 797–803. (Scholar)
  • –––, 1990, “Intuitionism as generalization”, Philosophia Mathematica, 5: 124–128. (Scholar)
  • –––, 1996, “Interview with a constructive mathematician”, Modern Logic, 6: 247–271. (Scholar)
  • –––, 2000, “The Fundamental Theorem of Algebra: A Constructive Treatment Without Choice”, Pacific Journal of Mathematics, 196: 213–230. (Scholar)
  • Riesz, F., 1908, “Stetigkeitsbegriff und abstrakte Mengenlehre”, Atti IV Congresso Internationale Matematica Roma II, 18–24. (Scholar)
  • Sambin, G., 1987, “Intuitionistic formal spaces—a first communication”, in Mathematical Logic and its Applications, D. Skordev (ed.), 187–204, New York: Plenum Press. (Scholar)
  • –––, forthcoming, The Basic Picture: Structures for Constructive Topology, Oxford: Oxford University Press. (Scholar)
  • Sambin, G., and Smith, J. (eds.), 1998, Twenty Five Years of Constructive Type Theory, Oxford: Clarendon Press. (Scholar)
  • Schuster, P.M., 2005, “What is continuity, constructively?”, Journal of Universal Computer Science, 11: 2076–2085 (Scholar)
  • –––, 2006, “Formal Zariski topology: positivity and points”, Annals of Pure and Applied Logic, 137: 317–359. (Scholar)
  • Schwichtenberg, H., 2009, “Program extraction in constructive analysis”, in Logicism, Intuitionism and Formalism—what has become of them?, S. Lindström, E. Palmgren, K. Segerberg, and V. Stoltenberg-Hansen (eds.), Berlin: Springer Verlag, 255–275. (Scholar)
  • Simpson, S.G., 1984, “Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations”, Journal of Symbolic Logic, 49(3): 783–802. (Scholar)
  • –––, 2009, Subsystems of Second Order Arithmetic, second edition, Cambridge: Cambridge University Press. (Scholar)
  • Specker, E., 1949, “Nicht konstruktiv beweisbare Sätze der Analysis”, Journal of Symbolic Logic, 14: 145–158. (Scholar)
  • Steinke, T.A., 2011, Constructive Notions of Compactness in Apartness Spaces, M.Sc. Thesis, University of Canterbury, Christchurch, New Zealand. (Scholar)
  • Troelstra, A.S., 1978, “Aspects of Constructive Mathematics”, in Handbook of Mathematical Logic, J. Barwise (ed.), Amsterdam: North-Holland. (Scholar)
  • Troelstra, A.S., and van Dalen, D., 1988, Constructivism in Mathematics: An Introduction (two volumes), Amsterdam: North Holland. (Scholar)
  • van Atten, M., 2004, On Brouwer, Belmont: Wadsworth/Thomson Learning. (Scholar)
  • van Dalen, D., 1981, Brouwer’s Cambridge Lectures on Intuitionism, Cambridge: Cambridge University Press. (Scholar)
  • –––, 1999, Mystic, Geometer and Intuitionist: The Life of L.E.J. Brouwer (Volume 1), Oxford: Clarendon Press. (Scholar)
  • –––, 2005, Mystic, Geometer, and Intuitionist: The Life of L.E.J. Brouwer (Volume 2), Oxford: Clarendon Press. (Scholar)
  • van Stigt, W.P., 1990, Brouwer’s Intuitionism, Amsterdam: North-Holland. (Scholar)
  • Vickers, S., 2005, “Localic completion of generalized metric spaces I”, Theory and Applications of Categories, 14(15): 328–356. (Scholar)
  • Waaldijk, F., 2005, On the foundations of constructive mathematics, Foundations of Science, 10(3): 249–324. (Scholar)
  • Wallman, H., 1938, “Lattices of topological spaces”, Annals of Mathematics, 39: 112–126. (Scholar)
  • Weihrauch, K., 2000, Computable Analysis (EATCS Texts in Theoretical Computer Science), Heidelberg: Springer Verlag. (Scholar)
  • Weyl, H., 1946, “Mathematics and Logic”, American Mathematical Monthly, 53(1): 2–13. (Scholar)
  • Whitehead, A.N., 1919, An Enquiry Concerning the Principles of Natural Knowledge, Cambridge: Cambridge University Press, second edition, 1925. (Scholar)

Related Literature

Generated Sun Nov 27 14:40:48 2022