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. Colorado Massacre Another Easy Problem Redesign in progress A simple problem ... Who wrote that? Me About this site My Work My Project My Department ... My Wishlist Recent Past Jan 2002 Dec 2001 Nov 2001 Oct 2001 ... Mar 2001 Distant Past Feb 2001 Jan 2001 Dec 2000 Nov 2000 ... Mar 2000 Them 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 New titles email For updates on new titles in: Pure Mathematics Philosophy of Mathematics Selected Readings 2nd Edition Edited by Paul Benacerraf, Hilary Putnam Paperback Contributors 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 Contents Cambridge University Press 2001. Security 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) Previous message: [Phil-logic] Re:Intuitionism-Heyting Next message: [Phil-logic] Re:Intuitionism-Heyting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] 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. Previous message: [Phil-logic] Re:Intuitionism-Heyting Next message: [Phil-logic] Re:Intuitionism-Heyting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

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 - Biografie (Philosophenlexikon.de) - Biografie (Philosophenlexikon.de) Habrotelia von Tarent - Biografie (Philosophenlexikon.de) Haeckel, Ernst - Biografie (Philosophenlexikon.de) Haecker, Theodor - Biografie (Philosophenlexikon.de) - Biografie (Philosophenlexikon.de) Hahn, Hans - Biografie (Philosophenlexikon.de) Haldane, John Scott - Biografie (Philosophenlexikon.de) Hallier, Ernst - Biografie (Philosophenlexikon.de) Hamann, Johann Georg - Biografie (Philosophenlexikon.de) Hamelin, Ostave - Biografie (Philosophenlexikon.de) Hamilton, William - Biografie (Philosophenlexikon.de) Hannequin, Arthur - Biografie (Philosophenlexikon.de) Hansch, Michael Gottlieb - Biografie (Philosophenlexikon.de) Hardenberg, Friedrich Leopold von - Biografie (Philosophenlexikon.de) Hare, Richard Mervyn - Biografie (Philosophenlexikon.de) Harms, Friedrich - Biografie (Philosophenlexikon.de) Hart, Herbert Lionel Adolphus

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