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         Heyting Arend:     more detail
  1. Intuitionism, An Introduction: Third Revised Edition by Arend Heyting, 2011-01-20
  2. Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (Studies in logic and the foundations of mathematics) by Arend Heyting, 1959
  3. Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01
  4. Semantical Investigations in Heyting's Intuitionistic Logic (Synthese Library) by Dov M. Gabbay, 1981-03-31
  5. ERKENNTNIS, Zugleich Annalen der Philosophie... BAND 2, HEFT 2-3, 1931; Bericht über die 2. Tagung für Erkenntnishlehre der exakten Wissenschaften Königsberg 1930 by Rudolf & Hans Reichenbach, eds. Arend Heyting, Johann von Neumann, Otto Carnap, 1931
  6. Mathematische Grundlagenforschung Intuitionismus-Beweistheorie by A. [Arend] HEYTING, 1980

21. Heijting
L AS Troelstra, 'arend heyting and his contribution to intuitionism', in NieuwArchief voor Wiskunde 3e serie 29 (1981) 1 23; idem, 'Logic in the writings
http://www.inghist.nl/Nieuws/Tips/Onderzoek/Projecten/BWN/lemmata/bwn3/heijting
@import url(CSS/Form); /*IE and NN6x styles*/ @import url(http://www.inghist.nl/Onderzoek/Projecten/BWN/lemmata/bwnstylesheet); /*IE and NN6x styles*/ HOME REACTIE SITEMAP HULP ... VERWIJZINGEN PROJECTMENU Biografie van Heijting, Arend Onderzoek Projecten Biografisch Woordenboek van Nederland heijting Biografisch Woordenboek van Nederland 3 (Den Haag 1989).
URL: http://www.inghist.nl/Nieuws/Tips/Onderzoek/Projecten/BWN/lemmata/bwn3/heijting
HEIJTING, Arend (1898-1980)
Heijting, Arend Na in 1922 cum laude het doctoraal examen te hebben afgelegd werd hij leraar aan het Gemeentelijk Lyceum te Enschede, waar hij o.a. wiskunde gaf. Daarnaast werkte hij aan zijn proefschrift, Die formalen Regeln der intuitionistischen Logik en Die formalen Regeln der intuitionistischen Mathematik Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie, bedoeld als bondig overzicht, verscheen in 1934, maar zou later in 1955 een bewerkte vertaling in het Frans beleven en in 1974 een Duitse tweede druk. In 1948 volgde Heyting zijn leermeester Mannoury op als gewoon hoogleraar in de wiskunde, en als zodanig trad hij nu ook op andere wijze naar voren, ofschoon hij als wetenschapsman uiteraard eveneens werkzaam bleef. Op wetenschappelijk gebied moet vooral genoemd worden de publikatie in 1956 van zijn zeer invloedrijke

22. Heyting-Algebra
Translate this page heyting-Algebra (arend heyting, 1898 - 1980). Unter einer heyting-Algebra(H, , , ,0,1) versteht man eine nichtleere Menge H mit
http://www.mathe.tu-freiberg.de/~hebisch/cafe/algebra/heytingalg.html
Heyting-Algebra (Arend Heyting, 1898 - 1980)
Unter einer Heyting-Algebra (H, versteht man eine nichtleere Menge H , einer Infimumsbildung und einer Implikation , sowie zwei ausgezeichneten Elementen und aus H x, y, z aus H (H, ist ein distributiver Verband x und x x x = 1, (x y) y = y und x (x y) = x y, x (y z) = (x y) (x z) und (x y) z = (x z) (y z). Brouwersche Algebren a b allerdings b : a Aus den Absorptionsgesetzen in dem (distributiven) Verband (H, und (2) folgen sofort x = x (x 0) = x und x 1 = x (x 1) = x (H,
  • Ist (H, eine Boolesche Algebra und definiert man a b = a' b a, b aus H , so wird (H, eine Heyting-Algebra.
  • 23. Lebensdaten Von Mathematikern
    Translate this page 1871) Herstein, Israel (1923 - 1988) Hesse, Ludwig Otto (22.4.1811 - 4.8.1874) vanHeuraet, Hendrik (1633 - 1660) heyting, arend (1898 - 1980) Hilbert, David
    http://www.mathe.tu-freiberg.de/~hebisch/cafe/lebensdaten.html
    Diese Seite ist dem Andenken meines Vaters Otto Hebisch (1917 - 1998) gewidmet. By our fathers and their fathers
    in some old and distant town
    from places no one here remembers
    come the things we've handed down.
    Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909)
    Abel, Niels Henrik (5.8.1802 - 6.4.1829)
    Abraham bar Hiyya (1070 - 1130)
    Abraham, Max (1875 - 1922)
    Abu Kamil, Shuja (um 850 - um 930)
    Abu'l-Wafa al'Buzjani (940 - 998)
    Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843)

    24. Player Summary Name Arend Heyting Gender M Occupation
    index recent most read by year by genre links stories guestbook. PlayerSummary. Name, arend heyting. Gender, M. Occupation, Mathematician. Born/Died, 00.
    http://www.y-intercept.com/player.html?player_id=227

    25. Bibast.html
    28, 63113. 1981 arend heyting and his contribution to intuitionism,Nieuw Archief voor Wiskunde (3) 29, 123. 1981A (with J. Niekus
    http://staff.science.uva.nl/~anne/bibast.html
    BIBLIOGRAPHY OF A.S. TROELSTRA Books Principles of intuitionism 1973 (with C.A. Smorynski, J.I. Zucker, W.A.Howard) Metamathematical Investigationof intuitionistic Arithmetic and
    Analysis
    , Springer Verlag, Berlin, 1323. Chapters IIV were written by A.S. Troelstra. A 2nd corrected edition appeared in 1993, as a report: ILLC Prepublication Series X-93-05, Universiteit van Amsterdam. Choice Sequences, a Chapter of Intuitionistic Mathematics , Clarendon Press, Oxford. 170 pages. 1988 (with D. van Dalen) Constructivismin Mathematics. An Introduction , Amsterdam, North-Holland Publ. Co. Vol.1: xx + 342 + XIV pages; Vol. 2: xviii + pages 345880 + LII pages. Lectures on Linear Logic , CSLI Stanford, Lecture Notes Series nr. 29. 1996A (with H. Schwichtenberg) Basic ProofTheory , Cambridge University Press, Cambridge U.K.
    Second, revised edition 2000. Papers 1965 Over een stelling van P. Zeeman en een stelling uit de affiene meetkunde (Dutch), Nieuw Tijdschrift voor Wiskunde 1965A On intermediate propositional logics

    26. Biographien - Archiv
    Translate this page h/heyne_c_g.shtml Heyse http//gutenberg.spiegel.de/autoren/heyse.htm Heyse, Paulhttp//www.dhm.de/lemo/html/biografien/HeysePaul/ heyting, arend http//www
    http://www.biografien-im-netz.de/archiv.php?Letter=H&Page=950

    27. Consequently.org
    consequently.org. 2001/11/16. arend heyting (18981980). arend heytingwas a brilliant Dutch logician beardless, as you can see - the
    http://consequently.org/archive/2001/11/16
    consequently.org
    Arend Heyting (1898-1980) Arend Heyting was a brilliant Dutch logician: beardless, as you can see - the Return of the Beards will be quite some decades to come. Heyting's claim to fame was to do something quite against the spirit of the intuitionist enterprise, but which made intuitionism a respectable and living (if minority ) tradition in logic. Heyting formalised intuitionistic logic. That is, he codified the kinds of inferences which are warranted by the lights of an intuitionist. This made "intuitionistic logic" an object of study, amenable to many of the same techniques that Frege and others had developed for the dominant tradition in logic, which we now call "classical" logic. More information about Heyting can be found at the St. Andrews' History of Mathematics Entry on him.
    Us
    There are 11 topics in total at consequently.org/discuss . Here are the recent topics.
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    the public record Continental Philosophy: A Very Short Introduction This is my personal space on the web. I think of it as an annotated bookmarks page, a scratchpad for thoughts and ideas, a place to post photos and somewhere to experiment with web design. I also use it to keep in touch with friends far away. The little datestamp on each entry takes you to the archived version of that entry. Use that if you want to link to an entry, as links to the main page expire when the entry rolls off the bottom of the page.

    28. Consequently.org
    More information about Curry can be found at the St Andrews' Historyof Mathematics Entry on him. 2001/11/16. arend heyting (18981980).
    http://consequently.org/archive/2001/11/
    consequently.org
    Jon Barwise (1942-2000) Jon Barwise was a renaissance logician . He didn't know everything but his contributions ranged so widely that he approximated omniscience quite well. His work ranges from infinitary logic (an extension of Frege-style predicate logic to deal with infinitely long sentences, and infinitary quantifiers), the model theory of first-order logic (continuing on from Tarski's work), generalsed quantifiers (quantifiers other than "for all" and "for some"), admissible sets and generalised recursion theory (the connections between sets and computation), situation semantics and the philosophy of language (using situations , restricted parts of the world as bearers of information, rather than just entire possible worlds), information theory (an account of how information flows and is transmitted), and the logic of diagrams (examining visual representation and inference, as well as linguistic representation). Barwise's work, in all of 35 years, has covered a huge range of disciplines, and it gives you some idea of the breadth of work available in contemporary logic. Barwise's approach of regularly moving into new fields, to keep fresh and active, is a helpful antidote in the current age of increasing specialisation and narrowing. If work like this is possible at the end of the 20th Century, it will be our job to see what might be done in the 21st. More information about Barwise can be found at the Barwise Memorial Pages at Indiana.

    29. Title Details - Cambridge University Press
    Rudolf Carnap, arend heyting, Johann von Neumann, LEJ Brouwer, Michael Dummett, GottlobFrege, Bertrand Russell, David Hilbert, Haskell B. Curry, Georg Kreisel
    http://books.cambridge.org/0521227968.htm
    Home Catalogue
    Related Areas: Pure Mathematics
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    Pure Mathematics
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    Rudolf Carnap, Arend Heyting, Johann von Neumann, L. E. J. Brouwer, Michael Dummett, Gottlob Frege, Bertrand Russell, David Hilbert, Haskell B. Curry, Georg Kreisel, Paul Bernays, Paul Benacerraf, Hilary Putnam, Alfred Jules Ayer, W. V. Quine, Carl G. Hempel, Henri Poincaré, Kurt Gödel, George Boolos, Hao Wang Email friend about this title
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    Order by phone (+44 (0)1223 326050) or fax (+44 (0)1223 326111).

    30. [Phil-logic] Re:Intuitionism-Heyting
    Vollstandigkeit der Principia ist die Vollstandigkeit meines Systems ME in der bestmoglichen Weise gesichert. , quoted in AS Troelstra, arend heyting and His
    http://philo.at/pipermail/phil-logic/2001-September/000031.html
    [Phil-logic] Re:Intuitionism-Heyting
    Graham Solomon gsolomon@wlu.ca
    Wed, 26 Sep 2001 12:48:37 -0400 (EDT) axioms, and deleted those which he thought are nonconstructive. That is hardly possible. Hilbert-Ackermann would seem a more likely source of inspiration. Yes, I likely misremembered the story.

    31. Spreads And Choice In Constructive Mathematics
    1 BISHOP, ERRETT AND DOUGLAS BRIDGES, Constructive analysis, SpringerVerlag1980. 2 heyting, arend, Intuitionism, an introduction, North-Holland 1956.
    http://www.math.fau.edu/Richman/docs/spreads.htm
    Spreads and choice in constructive mathematics
    Fred Richman
    Florida Atlantic University
    Boca Raton, FL 33431
    21 June 2001
    Abstract
    An approach to choice-free mathematics using spreads: If constructing a point satisfying property P requires choice, replace this problem by that of constructing a nonempty set of elements satisfying P . Then construct a spread, without choice, whose elements satisfy P . The theory is developed and several examples are given.
    Constructing points without choice
    There are many situations in (constructive) mathematics where you want to construct a point, say a real or complex number, with certain characteristics. The three problems I want to consider are
    • constructing a complex number that satisfies a given nonconstant polynomial over the complex numbers-the fundamental theorem of algebra
    • constructing a point in a given set of positive measure, and
    • constructing a point in the intersection of a given countable family of open dense subsets of a complete metric space-the Baire category theorem.
    For each of these problems, the traditional solutions appeal to countable choice, or rather to the stronger

    32. Former News And Events 2001
    Provisional Programme 13.3013.45 Reception with tea, coffee 13.45-14.00 Introductionby the chairman of the arend heyting Foundation 14.00-15.00 F. Richman
    http://www.illc.uva.nl/NewsandEvents/formernews.php?year=2001

    33. Bio-/Biblio-graphical Details Of Authors Whose Names Start With H
    H. Hesse Siddharta , New directions, New York, 1951, p. 83; Ibid.p. 17. Ibid., p. 110; Ibid., p. 17. heyting, arend. REF A heyting
    http://mpec.sc.mahidol.ac.th/preedeeporn/AuthorsH.HTM

    34. Abdu'l Baha Abelard, Peter Abelson, PH Acheson, Dean Gooderham
    Hess, Harry Hammond Hesse, Hermann heyting, arend Hilbert, David Hill, Thomas Hillary,Sir Edmund Hinshelwood, Sir Cyril Norman Hippocrates Hirsch, Morris W.
    http://mpec.sc.mahidol.ac.th/preedeeporn/Authrsaz.HTM

    35. Biography-center - Letter H
    1910/heyseautobio.html; heyting, arend www-history.mcs.st-and.ac.uk/~history/Mathematicians/heyting.html;Hibbard, Aldro Thompson
    http://www.biography-center.com/h.html
    Visit a
    random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish
    H
    703 biographies

    • www-history.mcs.st-and.ac.uk/~history/Mathematicians/Herigone.html
    • www-history.mcs.st-and.ac.uk/~history/Mathematicians/De_L'Hopital.html
    • www-history.mcs.st-and.ac.uk/~history/Mathematicians/Holder.html
    • www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hormander.html
    • Haab, Otto
      www.whonamedit.com/doctor.cfm/1825.html
    • Haanpää, Pentti
      www.kirjasto.sci.fi/haanpaa.htm
    • www-history.mcs.st-and.ac.uk/~history/Mathematicians/Haar.html
    • Haarlem, Cornelis van www.kfki.hu/~arthp/bio/c/cornelis/biograph.html
    • Haavelmo, Trygve www.nobel.se/economics/laureates/1989/haavelmo-bio.html
    • Haavikko, Paavo www.kirjasto.sci.fi/haavikko.htm
    • Haber, Fritz www.nobel.se/chemistry/laureates/1918/haber-bio.html
    • Habib ibn Zayd al-Ansari,

    36. References
    heyting 30 arend heyting. Die formalen Regeln der intuitionistischen Logik. Sitzungsber.Preuss. Akad. heyting 56 arend heyting. Intuitionism An Introduction.
    http://www.cs.cornell.edu/Info/Projects/NuPrl/book/node249.html
    Next: Index Up: No Title Previous: Appendix C: Direct
    References
    Aczel 77

    Peter Aczel.
    An introduction to inductive definitions.
    In Handbook of Mathematical Logic , J. Barwise, ed.
    NorthHolland, Amsterdam, 1977, pages 739782.
    Aczel 78

    Peter Aczel.
    The type theoretic interpretation of constructive set theory.
    In Logic Colloquium '77
    A. MacIntyre, L. Pacholaki, and J. Paris, eds.
    NorthHolland, Amsterdam, 1978, pages 5566.
    Alfred V. Aho and J. E. Hopcroft and J. D. Ullman. The Design and Analysis of Computer Algorithms AddisonWesley, Reading, MA, 1974. L. Aiello, M. Aiello, and R. W. Weyhrauch. Pascal in LCF: semantics and examples of proof. Theoretical Computer Science , v. 5, n. 2 (1977) pages 135178.
    Allen 86
    Stuart F. Allen. The Semantics of Type Theoretic Languages. Doctoral Dissertation, Computer Science Department, Cornell University, August 1986 (expected). John M. Anderson and Henry W. Johnstone. Natural Deduction Wadsworth, Belmont, CA, 1962.
    Andrews 65
    P. B. Andrews. Transfinite Type Theory with Transfinite Type Variables. NorthHolland, Amsterdam, 1965.

    37. CS 486: Applied Logic
    arend heyting showed that these propositions form the core of firstorder logicand arithmetic, and that Peano arithmetic (PA) can be factored into heyting
    http://www.cs.cornell.edu/Courses/cs486/2001SP/Summary/summary.html
    CS 486: Applied Logic
    Spring 2001
    Summary
    Major Topics
    • Propositional Calculi (Classical and Intuitionistic) - Smullyan book
      • Analytic tableau
      • Completeness and decidability
      • Gentzen Systems/Sequents/Refinement Logics
      • Formal proof of decidability
      • Proof expressions
      • Second-order propositional logic, system F

    • Predicate Calculi (Classical and Intuitionistic) - Smullyan book

      • Specification Language
      • Completeness and Compactness Theorems
      • Fundamental Theorem
      • Church's Theorem
    • Formal Number Theory (Peano Arithmetic (PA) and Heyting Arithmetic (HA)) : Suppes book
    • Set Theory (ZF and IZF) : Suppes book
    • Typed and Higher Order Logics (Type Theory and Class Theory) : Lecture Notes and Nuprl web page
    • Programming Logics : Lecture Notes
    • : Handout
    • Special topics as possible
    Connection to Computer Science
    The driving idea is to use CS background as a springboard to get deep into parts of logic by recasting them in CS terms. This is a CS course that shows how logic is an integral part of CS (AI, systems, program verification, programming languages), and CS recasts large parts of logic in its own terms computabilitiy, specification, verification, model checking, intelligent systems, automated reasoning.
    Background
    Logic is concerned with propositions and proofs , just as number theory is concerned with natural numbers and operations on numbers. A proposition is an abstract mathematical object corresponding to a declarative sentence. We speak of the

    38. 148 Syll 2003
    Intuitionism and the Hilbert program. arend heyting, The intuitionist foundationsof mathematics, in B P, pp. 5261. arend heyting, Disputation, in B P.
    http://icg.harvard.edu/~phil148/syllabus/148_Syll_2003.html
    HARVARD UNIVERSITY Department of Philosophy
    Philosophy 148: Philosophy of Mathematics
    Spring Term 2003 Professor Charles D. Parsons
    Emerson 201, tel. 495-8337
    parsons2@fas.harvard.edu Prerequisities: Students should have a knowledge of elementary logic (e. g. Quantitative Reasoning 22), but a strong mathematics background would compensate for such lack. Students should purchase the following books: Paul Benacerraf and Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings Gottlob Frege, The Foundations of Arithmetic . Evanston, Northwestern University Press. (Originally Blackwell, Oxford, 1953; German text Breslau 1884.) Other readings will be on reserve in Robbins Library (second floor of Emerson). Two books intended as introductions to the philosophy of mathematics have been published recently: Stewart Shapiro, Thinking about Mathematics (Oxford University Press, 2000), and Alexander George and Daniel J. Velleman, Philosophies of Mathematics Written work : One or two short papers on prescribed topics will be assigned during the term. A term paper on a topic of your own choice will be due during the reading period. You are urged to discuss your topic with me early in your work on this paper. There will be a final examination, most likely take-home.

    39. Squangles
    Fünfte Auflage. Braunschweig Friedrich Vieweg und Sohn, 1903. heyting, arend. Intuitionism.An Introduction. Amsterdam NorthHolland, 1958. Kant, Immanuel.
    http://www.cwi.nl/projects/alp/newsletter/nov01/nav/squangles/squangles.html
    Squangles Henk Visser IKAT, Universiteit Maastricht
    COMP. Good morning Math, what can I do for you?
    MATH. Nothing at all, but I want to show you something.
    COMP. Go ahead, my computer can wait.
    MATH. Do you remember my Transpositional Tricks?
    COMP. Of course, I liked your geometrical pictures, do you have more of those nice things?
    MATH. In a way, yes, but let me first of all state the problem. You know that I found a beautiful representation of the equation 666 = 441 + 225, which I analyzed as an equation between the triangular number of a square - 36 - and the squares of two successive triangular numbers - 15 and 21. Well, when I looked at the tables of the squares and the triangular numbers, I noticed that 36 occurs in both of them and so I wondered whether there are more squares that are also triangles. By the way, I call such numbers squangles.
    COMP. Was this your problem? Wait a moment and my computer will give you the answer!
    MATH. Stop, this is not a computational problem. I wanted to have insight into the mathematics behind the equation s(m) = t(n), I am not interested in the solutions as such.
    COMP. I see, tell me what you've found.

    40. Mair.net - Philosophen - H
    heyting, arend - Biografie (Philosophenlexikon.de);Hieronymos aus Rhodos - Biografie (Philosophenlexikon.de); Hilbert
    http://mair.net/Wissenschaft/philosophe9.htm
    Internetverzeichnis
    Wetter
    Nachrichten Homepage anmelden Tipps zur Suche ... Hilfe
    mit Standardsuche mit Meta-Suche
    Mair.net
    Philosophie Philosophen : Philosophen - H : Philosophen - H

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