61. CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS [1] Eindhoven 23 7 Amsterdam (The Netherlands) 1426 September 1998 arend heyting CentenaryPROGRAM heyting Lectures, heyting Symposium, Thematic Day http://colibri.let.uu.nl/html/html.24-1998/general.html

CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS Eindhoven 23 June 1998 ZIC Colloquium on Logic and Theoretical Computer Science dr. ir. Hans de Nivelle: "Implementation of a resolution theorem prover" Montpellier (France) 10-12 August 1998 ICCS'98 6th International Conference on Conceptual Structures CALL FOR PARTICIPATION Saarbruecken (Germany) 14-16 August 1998 FHCG-98 Joint Conference on Formal Grammar, Head-driven Phrase Structure Grammar and Categorial Grammar PROGRAM Saarbruecken (Germany) 14-16 August 1998 FHCG-98 Joint Conference on Formal Grammar, Head-driven Phrase Structure Grammar and Categorial Grammar PROGRAM Melbourne (Australia) 28 August 1998 ACM-SIGIR'98 Post-Conference Workshop on "Multimedia Indexing and Retrieval" EXTENDED Deadline: 19 June 1998 Freiburg (Germany) 7-9 September 1998 LD'98 The First International Workshop on Labelled Deduction http://www.informatik.uni-freiburg.de/~ld98 CALL FOR PARTICIPATION Amsterdam (The Netherlands) 14-26 September 1998 Arend Heyting Centenary PROGRAM: Heyting Lectures, Heyting Symposium, Thematic Day

62. Philosophy Of Mathematics Class Notes PHL-113 Dr. Carl Posy Duke arend heyting(55) said the role of a math teacher is to make the student carry Brouwer s disciple, arend heyting, took on the challenge of explaining to http://www.badros.com/greg/doc/philmath.htm

Philosophy of Mathematics Class Notes PHL-113 Dr. Carl Posy Duke University Fall 1992 Prepared by Greg J. Badros Table of Contents Part I: General Survey of Philosophy of Mathematics 1 I.1 Prehistory of numbers 1 I.2 Greek Development of Math 2 2.1 Flowering of the Pythagoreans 3 2.2 Downfall of the Pythagoreans 3 2.3 Greek Reaction to the Downfall 4 I.3 Road to Non-Euclidean Geometry 12 3.1 Hilbert's axiomatization of Geometry 12 3.2 The Evaluation of non-Euclidean Geometry 13 I.4 History of the concept of a number 16 I.5 Conceptual Foundations of Mathematics 22 5.0 General Overview of Reactions to Berkeley 23 5.0.1 Kant's Philosophy of Mathematics 24 5.1.1 Introduction of the Notion of a Limit 25 5.1.2 Arithmetization of Mathematics 26 5.2 Cantor 29 5.3.1 Peano 33 5.3.2 Frege 34 I.6 Two of the Three Reactions to the Third Crisis 37 6.1 Platonistic Reaction 37 6.2 Hilbert's Program 40 Part II: Intuitionism, A Third Direction 46 II.1 General Introduction to Intuitionism 46 II.2 Intuitionist's Construction of the Natural Numbers 47 II.3 Intuitionist's Construction of the Real Numbers 47

63. What Do Types Mean? In arend heyting, editor, Constructivity in Mathematics, pages 101128.North-Holland, Amsterdam, 1959. 14 14 SC Kleene. Countable functionals. http://portal.acm.org/citation.cfm?id=766967

64. AIP International Catalog Of Sources Correspondents include Paul Bernays, William Boone, Rudolf Carnap, Paul J.Cohen, Gotthard Gunther, Jacques Herbrand, arend heyting, Georg Kreisel, http://www.aip.org/history/catalog/156.html

If you are not immediately redirected, please click here My List - Help Browse Archival Resources Archival Finding Aids Books Photos Browse FAQs Past Searches History Home Search: Author Subject Title Journal/Newspaper Title Series Computer File (Software) Title Video Title Refine Search AIP Niels Bohr Library Item Information Holdings More by this author Subjects Logic, Symbolic and mathematical. Mathematical physics. Mathematics Problems, exercises, etc. Mathematics Research New Jersey Princeton 20th century. Mathematics, German. Browse Catalog by author: by title: MARC Display by Description: 30.50 cu. ft. (43 boxes, 9 cartons, 1 oversized box, 1 package) Use and Reproduction : No Xeroxing is allowed, except with prior written permission of the Institute for Advanced Study. Owning Repository: Princeton University. Dept. of Rare Books and Special Collections, One Washington Road, Princeton, NJ 08544 USA. Country of Repository: USA Biography/History: Scope of Material: Provenance: Arrangement of Records: Notes: Finding Aid: Preservation microfilm is available for Series I. through XIV. An 81-page finding aid is available. also available in the AIP Niels Bohr Library. Added Author: AIP-ICOS Genre Term(s): Notebooks.

65. Practical Foundations Of Mathematics REMARK 2.4.3 arend heyting and Andrei Kolmogorov independently gave thisinterpretation of intuitionistic logic in 1934. To prove http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/s24.html

Practical Foundations of Mathematics Paul Taylor Propositions as Types Although the predicate calculus underlies Zermelo type theory, it is always foolish to assert that one piece of mathematics is more basic than another, because a slight change of perspective overturns any such rigid orders. Indeed Jan Brouwer (1907) considered that logical steps rest on mathematical constructions. One of the most powerful ideas in logic and informatics in recent years has been the analogy between =0pt omitted tabular environment which puts propositions and types on a par. This is sometimes called the Curry-Howard isomorphism Formulae correspond to types and their deductions to terms. Crudely, a type gives rise to the proposition that the type has an element, and a proposition to the type whose elements are its proofs. Indeed, as soon as we take some care over it, we have no alternative but to treat the hypothesis for alongside the generic value of and the bound variable of l . Similarly Sections and show that midconditions go with program-variables. Other analogies with types

66. Practical Foundations Of Mathematics Hey56 arend heyting. Intuitionism, an Introduction. Studies in Logic and theFoundations of Mathematics. NorthHolland, 1956. Revised edition, 1966. http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/bib.html

Practical Foundations of Mathematics Paul Taylor Chapter 9 Bibliography Samson Abramsky and Achim Jung. Domain theory. In Samson Abramsky et al., editors, Handbook of Logic in Computer Science , volume 3, pages 1-168. Oxford University Press, 1994. Peter Aczel. Non-well-founded Sets . Number 14 in Lecture Notes. Center for the Study of Language and Information, Stanford University, 1988. Locally Presentable and Accessible Categories . Number 189 in London Mathematical Society Lecture Notes. Cambridge University Press, 1994. Pierre Ageron. The logic of structures. Journal of Pure and Applied Algebra Thorsten Altenkirch, Martin Hofmann, and Thomas Streicher. Categorical reconstruction of a reduction-free normalisation proof. In Peter Johnstone, David Pitt, and David Rydeheard, editors, Category Theory and Computer Science VI , number 953 in Lecture Notes in Computer Science, pages 182-199. Springer-Verlag, 1995. Roberto Amadio and Pierre-Louis Curien. Domains and Lambda-Calculi . Number 46 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1998.

67. MathComp Database - Browse - List 10, Heyer, Herbert. 8, heyting, A. (arend), 1898. 8, heyting, arend, 1898-See $$aheyting, A.$$q(arend),$$d1898-. 5, Heywood, JG (John Groves), 1940- http://ram0.huji.ac.il/ALEPH/ENG/JSL/JMC/JMC/SCAN-R/0402532

MathComp database - Browse - AUTHOR list - ALL DOCUMENTS The numbers in the list below indicate the number of documents listed under a term. To display the documents, click on an eye . To move up or down the list, click on the arrow. Heterogeneous Computing Workshop (9th : 2000 : Cancun, Mexico) Heudin, J. C. Hewitt, Edwin, 1920- Hewitt, G. F. (Geoffrey Frederick) Hewlett, Walter B. Hey, Anthony J. G. Heyd, Michael Heyde, C. C. Heyer, Herbert Heyting, A. (Arend), 1898- Heyting, Arend, 1898- See: $$aHeyting, A.$$q(Arend),$$d1898- Heywood, J. G. (John Groves), 1940-

68. Www.searchword.org/ar/arend-heyting.html PDF Literaturverzeichnis http://www.searchword.org/ar/arend-heyting.html

69. Filmmaking, Logic And The Historical Reconstruction Of The World Although arend heyting showed in 1930 that one could formally redefine negation 18 arend heyting, Die formlen Regeln der intuitionistischen Logic , http://www.hanover.edu/philos/film/vol_02/cameron.htm

Filmmaking, Logic and the Historical Reconstruction of the World Evan William Cameron Notes Return to Film and Philosophy , Volume II, Table of Contents

70. Historical Notes the existence of the sector was a Summer School and Conference on MathematicalLogic honourably dedicated to the 90th anniversary of arend heyting. http://www.fmi.uni-sofia.bg/fmi/logic/skordev/history.htm

Some short historical notes on Development of Mathematical Logic in Sofia by Dimiter Skordev Currently, mathematical logic in Bulgaria has some presence not only at Sofia, but also at several other university centres. However, I shall restrict myself only to its history in Sofia, since both the history and the present state of the field in those other places are far from being as abundant as in Sofia. In addition, I shall speak mainly about the earlier part of the history, since it is probably the less known to the audience. The year 1989 will be regarded as the end of that period of time. Besides, I shall actually speak mostly about the history of the Department of Mathematical Logic, meaning the former Sector of Mathematical Logic and the two currently existing units that succeeded it in 1989. In fact, almost all people who work or have worked in mathematical logic at Sofia either are present or former members of this department or have graduated from it . There are only a few exceptions. Bojan Petkanchin (1907-1987), a greatly respected professor in geometry at Sofia University, is one of them, and his pioneering role in the history of mathematical logic in Sofia will be considered further. Another exception is

71. Collected Works : Correspondence H-Z (Godel, Kurt//collected Works): ‹IˆÉš  Translate this page correspondence 433 (36) Correspondence included in these volumes 434 (13)Individual calendars of correspondence arend heyting 447 (2) Karl Menger 449 http://bookweb.kinokuniya.co.jp/htmy/0198500750.html

US:New York Times US:PublishersWeekly US:Brandon-Hill US:Library Journal ... ŸŠúŠÔŒÀ’è“Á‰¿ƒR[ƒi[ ˜a‘ —m‘ “dŽq‘Ð “X“ªÝŒÉ Kinokuniya DataBase Search Result matches Table of Contents Collected Works : Correspondence H-Z (Godel, Kurt//collected Works) -US- ISBN:0198500750 (Hard cover book) vol.005 Godel, Kurt Feferman, Solomon (EDT) Dawson, John W. (EDT) Goldfarb, /Publisher:Oxford Univ Pr Published 2003/05 ŠO‰Ý’艿:US$ 199.50 Price: (D) Qty. FAST DELIVERY ‚±‚̏¤•i‚́AŠCŠO‚̏‘ÐŽæŽŸ‰ïŽÐ‚ɍ݌ɂª‚²‚´‚¢‚Ü‚·B ’ʏíA (Science/Mathematics) Look for similar books by category Look for similar books by subject: Logic, Symbolic and mathematic šAcademic Title Information DDC: Source:ENG Academic Descriptors: Publishers : University Press Place of Publication : Great Britain Language of Publication : English Edition : First Physical Format : Hardbound Continuations : Sets,any number Textual Format : Readings/Anthologies Academic Level : Graduate Geographic Designator : Western Europe Table of Contents E-mail: webmaster@kinokuniya.com DATA

72. CASE Newsletter No.4 They include the papers of HA Lorentz (18531928), Pieter Zeeman (1865-1943), WHKeesom (1876-1956), arend heyting (1898-1980), Evert Willem Beth http://www.bath.ac.uk/ncuacs/casenl4.htm

Cooperation on Archives of Science in Europe Coopération pour les Archives Scientifiques en Europe NEWSLETTER No.4 December 1999 CONTENTS 1. INTRODUCTION 2. SCIENTIFIC ARCHIVES IN CATALONIA: NEW SERVEI D'ARXIUS DE CIÈNCIA 3. THE DUTCH CENTRE FOR SCIENCE ARCHIVES AT THE 'RIJKSARCHIEF IN NOORD-HOLLAND' IN HAARLEM 4. COLLABORATION BETWEEN THE ARCHIVES OF IMPERIAL COLLEGE LONDON AND THE INSTITUT PASTEUR, PARIS ... 7. ARCHIVES RECEIVE GRANTS FOR COLLECTIONS IN PHYSICS AND ALLIED FIELDS 1. INTRODUCTION The Newsletter goes from strength to strength. It may also be appropriate to mention a small number of items of CASE news. We are very pleased to welcome as a new member since the last Newsletter Paula Velthuys-Bechthold of the Rijksarchief in Noord Holland at Haarlem. To demonstrate that as a group we are not completely eurocentric I very willingly agreed to write a short article on CASE for the American Institute of Physics Center for the History of Physics Fall 1999 Newsletter. CASE was also a principal topic of my own paper at the Warsaw conference. I am once again very grateful to all those who have contributed to the success of the Newsletter with reports and information, and to my colleague Alan Hayward who is responsible for the CASE website and thus the appearance of this Newsletter on the Web.

73. Greg Restall * Great Moments In Logic... Image of heyting arend heyting was a brilliant Dutch logician beardless, asyou can see — the Return of the Beards will be quite some decades to come. http://consequently.org/archive/2001/11/

@import "2004.css"; consequently.org/writing/logicians Search this site home writing news archive zachary ... AJL Post a comment Name: Email Address: URL: Remember personal info? Yes No Comments: Great Moments in Logic Bernhard Bolzano (1781-1848) best known for what he has done in mathematics : the precise definition of continuity when it comes to real-valued functions. But for my money (and in my discipline) Bolzano was worth much more than this. He was the first philosopher to give a precise analysis of logical consequence in terms we would recognise today. (This was important for his project of understanding mathematics, and making it clearer, because mathematicians were getting into knots considering infinite numbers, infinitesimal Anyway, he argued that you can tell that an argument from premises to a conclusion is logically valid if and only if it never proceeds from truth to falsity no matter how you change the non-logical vocabulary in the argument. So Sally is coming to the party. If Sally is coming to the party, Jim will be happy. Therefore Jim will be happy.

74. Arend Heyting - Article And Reference From OnPedia.com People whose names are embedded in Math Subject Classifcation Berkeley AMWS http//math.berkeley.edu/faculty.html emeritus heyting,arend (18981980), P7b, WWS, TUF 91i01094 Kushner, BA arend heyting a short http://www.onpedia.com/encyclopedia/Arend-Heyting

Arend Heyting Arend Heyting May 9 July 9 ) was a Dutch mathematician and logician . He was a student of L. E. J. Brouwer , and did much to put intuitionistic logic on a footing where it could become part of mathematical logic (which in a definite sense ran counter to some of the initial intentions of its founder). He was born in Amsterdam Netherlands , and died in Lugano Switzerland See also Heyting algebra External link "Arend Heyting" in The MacTutor History of Mathematics Archive Heyting, Arend Heyting, Arend Heyting, Arend w('arend-heyting') Word Browser steve scherf intensive quantity christoph von dohnnyi kilcar ... east los angeles (region)

75. Currículo Do Sistema De Currículos Lattes (Oswaldo Chateaubriand Review of arend heyting Methodes et problémes de l intuitionisme . http://buscatextual.cnpq.br/buscatextual/visualizacv.jsp?id=K4783540J5

76. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï heyting, arend heyting Born 9May 1898 in Amsterdam, Netherlands Died 9 July 1980 in Lugano, Switzerland http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=H

77. Collected Works Added Entry heyting, A. (arend), 1898 CALL NO QA267 B79 1990 AUTHOR Buchi, J.Richard. TITLE Works. 1990 MAIN TITLE The collected works of J. Richard http://lib.nmsu.edu/subject/math/mbib.html

C OLLECTED W ORKS F M ATHEMATICIANS B IBLIOGRAPHY CALL NO: QA3 A14 1881 AUTHOR: Abel, Niels Henrik, 1802-1829. MAIN TITLE: OEuvres completes de Niels Henrik Abel. EDITION: Nouv. ed., publiee aux frais de l'etat norve-gien par L. Sylow PUBLISHER: Christiania [Sweden] Grondahl, 1881. LOCATION: Branson Material: 2 v. in 1. 28 cm. Contents: t. 1. Memoires publies par Abel.t. 2. Memoires posthumes d'Abel Subject: Mathematics. cm Added Entry: Sylow, Peter Ludvig Mejdel, 1832- Added Entry: Lie, Sophus, 1842-1899. CALL NO: QB3 A2 AUTHOR: Adams, John Couch, 1819-1892. MAIN TITLE: The scientific papers of John Adams Couch, edited by William Grylls Adams, with a memoir by J. W. L. Glaisher. PUBLISHER: Cambridge, University press, 1896-1900. LOCATION: Branson V.1 and V.2 Material: 2 v. front. (port.) fold. map, facsims., diagr. 30 cm. Contents: v. 1. Biographical notice, by J. W. L. Glaisher. [Original papers published by the author during his lifetime, 1844-1890, ed. by William Grylls Adams]v. 2. pt. 1. Extracts from unpublished manuscripts, ed. by Ralph Allen Simpson. pt. 2. Terrestial magnetism, ed. by William Grylls Adams. Subject: Geomagnetism.

78. Encyclopedia: Arend Heyting BauerPreisProfessor Troelstra is a scientific grandson of the famous mathematician andlogician Luitzen Egbertus Jan Brouwer; his academic teacher was arend heyting. http://www.nationmaster.com/encyclopedia/Arend-Heyting

Supporter Benefits Signup Login Sources ... Pies Related Articles People who viewed "Arend Heyting" also viewed: Heyting algebra Intuitionism Intuitionistic type theory Britpop What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Michael Pitfield Michael Moore Michael Copon Mettler toledo ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Arend Heyting Updated 6 days 8 hours 20 minutes ago. Other descriptions of Arend Heyting Arend Heyting May 9 July 9 ) was a Dutch mathematician and logician . He was a student of L. E. J. Brouwer , and did much to put intuitionistic logic on a footing where it could become part of mathematical logic (which in a definite sense ran counter to some of the initial intentions of its founder). May 9 is the 129th day of the year in the Gregorian Calendar (130th in leap years). ... 1898 was a common year starting on Saturday (see link for calendar). ... July 9 is the 190th day of the year (191st in leap years) in the Gregorian Calendar, with 175 days remaining. ... 1980 is a leap year starting on Tuesday. ...

79. Er Uendelighed Aktuel Eller Potentiel? heyting, arend ‘The Intuitionist Foundations of Mathematics’ (1931), heyting,arend Intuitionism – An Introduction (1971), tredje udgave, Amsterdam. http://www.filosofi.net/Afhandlinger/Html/uendelighed.htm

Uendelighed, aktuel eller potentiel? er et BA-projekt ved: Center for Filosofi, Filosofisk Institut Odense Universitet, Syddansk Universitet Af Lisbeth Jørgensen lisbeth_jorgensen@yahoo.com Vejleder: Cynthia M. Grund Forside: Georg Cantor og L.E.J.Brouwer set med uendelighedens brilleglas Afleveret d. 8/1 2001 Indholdsfortegnelse Problemformulering Indledning Uendelighedens paradokser Baggrundshistorien for distinktionen mellem aktuel og potentiel uendelighed ... Litteraturliste Problemformulering Er uendelighed aktuel eller potentiel? Hvad er argumenterne for at uendelighed er aktuel henholdsvis potentiel? Hvilke nye problemer udløser disse argumenter? Indledning Hvad er uendelighed? Findes uendelighed, er der noget uendeligt i verden? Eller er uendelighed bare noget vi bruger som begreb, en slags grænse som egentlig ikke er der. I det overordnede spørgsmål om hvad uendelighed er, ligger også en undersøgelse af tid og rum, men jeg vil i denne opgave begrænse mig til den matematiske uendelighed. Således hører denne opgave ind under matematikkens filosofi. Min filosofiske indgangsvinkel til dette emne er at tage udgangspunkt i de paradokser der opstår ved nærmere betragtning af uendelighed. Man kan så spørge hvilken opfattelse af uendelighed der har betydning for at de forskellige paradokser opstår. Kan de forskellige forklaringer af matematisk uendelighed give en løsning på paradokserne, uden at nye opstår? Uendelighed optræder i matematikken bl.a. i mængdelære og i geometri. Mængden af naturlige tal er uendelig stor; uanset hvor langt man tæller, er det altid muligt at tælle én til. Der er således ikke noget største naturligt tal – enhver kandidat til et sådant kan med det samme blive større ved at lægge én til. I geometriens studie af rummet kan en linje deles uendeligt mange gange, og ethvert interval kan blive underinddelt i flere underinddelinger. Den tanke at en proces kan fortsættes i det uendelige, introducerer uendelighed som potentiel; uendelighed er aldrig noget der kan nås. I vores standard aritmetik (tallære) opfattes uendelighed på den anden side også som aktuel: Mængden af naturlige tal opfattes som

80. Citebase - Quantitative Models And Implicit Complexity In arend heyting, editor, Constructiviey in Mathematics, pages 101128.North-Holland, 1959. G/A, 12 Yves Lafont. Soft linear logic and polynomial time. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:cs/0506079

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