1. Heyting Arend Heyting. Born 9 May 1898 Arend Heyting s father was Johannes Heytingand his mother was Clarissa Kok. Both Arend s parents were http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Heyting.html

Arend Heyting Born: 9 May 1898 in Amsterdam, Netherlands Died: 9 July 1980 in Lugano, Switzerland Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Arend Heyting 's father was Johannes Heyting and his mother was Clarissa Kok. Both Arend's parents were school teachers and Johannes Heyting was particularly successful in his profession being appointed as head of a secondary school. Arend spent his school years with the intention that he would make a career in engineering. Only near the end of his schooling did his love and ability in mathematics mean that the course of his career changed and he went to university to study mathematics. Although Heyting's father was a successful school teacher, the family were still in financial problems when Heyting began his studies in 1916 at the University of Amsterdam. Both Heyting and his father earned the extra money necessary to pay for his studies by taking on private tutoring work. At the University of Amsterdam Heyting was taught by Brouwer who had a large influence on his future work. In 1922 Heyting graduated with a degree of master's standard.

2. Poster Of Heyting Arend Heyting. lived from 1898 to 1980. Arend Heyting is importantin the development of intuitionistic logic and algebra. Find http://www-gap.dcs.st-and.ac.uk/~history/Posters2/Heyting.html

Arend Heyting lived from 1898 to 1980 Arend Heyting is important in the development of intuitionistic logic and algebra. Find out more at http://www-history.mcs.st-andrews.ac.uk/history/ Mathematicians/Heyting.html

3. Heyting Arend Heyting. Born 9 May 1898 Arend Heyting was taught by Brouwer whohad a large influence on his future work. He received his doctorate http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Hytng.htm

Arend Heyting Born: 9 May 1898 in Amsterdam, Netherlands Died: 9 July 1980 in Lugano, Switzerland Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Arend Heyting was taught by Brouwer who had a large influence on his future work. He received his doctorate in 1925 under Brouwer 's supervision and was appointed to Amsterdam in 1937. Heyting formalised Brouwer 's intuitionism, publishing on intuitionistic algebra in 1941 and intuitionistic Hilbert spaces in the 1950's. His important books include Intuitionism and Proof Theory (1934) and Intuitionism: an Introduction References (6 books/articles) Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Heyting.html

4. Haken Hermann SYNERGETICS (Springer-Verlag, 1977) The distributed system can only exhibit global coherence . heyting arendINTUITIONISM (North Holland, 1956). A classic textbook for intuitionism. http://www.thymos.com/mind/h.html

Haken Hermann: SYNERGETICS (Springer-Verlag, 1977) Synergetics is a theory of pattern formation in complex systems. It tries to explain structures that develop spontaneously in nature. Since order emerges out of chaos, and chaos is not well defined, synergetics employs probabilities (to describe uncertainty) and information (to describe approximation). Entropy becomes a central concept, relating physics to information theory. Synergetics revolves around the concepts of: compression of the degrees of freedom of a complex system into dynamic patterns that can be expressed as a collective variable; behavioral attractors of changing stabilities; and the appearance of new forms as nonequilibrium phase transitions. Systems at instability points are driven by a slaving principle: long-lasting quantities can enslave short-lasting quantities (i.e., they can act as order parameters). Close to instability, stable motions (or "modes") are enslaved by unstable modes and can be ignored, thereby reducing the degrees of freedom of the system. The macroscopic behavior of the system is determined by the unstable modes. The dynamic equations of the system reflect the interplay between stochastic forces ("chance") and deterministic forces ("necessity"). Synergetics deals with self-organization, how collections of parts can produce structures. Synergetics therefore applies to systems driven far from equilibrium, where the classic concepts of thermodynamics are no longer adequate. Order can arise from chaos and can be maintained by flows of energy/matter.

5. Biography-center - Letter H literature/laureates/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 745 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 Haas, Dolly www.cyranos.ch/emigra-e.htm#haas 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,

6. Thematic Afternoon On Constructivism Including the first arend heyting Lecture. Amsterdam, the Netherlands; 14 December 2001. http://turing.wins.uva.nl/~anne/heyting.html

7. Heyting Biography of arend heyting (18981980) arend heyting. Born 9 May 1898 in Amsterdam, Netherlands arend heyting's father was Johannes heyting and his mother was Clarissa Kok http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Heyting.html

Arend Heyting Born: 9 May 1898 in Amsterdam, Netherlands Died: 9 July 1980 in Lugano, Switzerland Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Arend Heyting 's father was Johannes Heyting and his mother was Clarissa Kok. Both Arend's parents were school teachers and Johannes Heyting was particularly successful in his profession being appointed as head of a secondary school. Arend spent his school years with the intention that he would make a career in engineering. Only near the end of his schooling did his love and ability in mathematics mean that the course of his career changed and he went to university to study mathematics. Although Heyting's father was a successful school teacher, the family were still in financial problems when Heyting began his studies in 1916 at the University of Amsterdam. Both Heyting and his father earned the extra money necessary to pay for his studies by taking on private tutoring work. At the University of Amsterdam Heyting was taught by Brouwer who had a large influence on his future work. In 1922 Heyting graduated with a degree of master's standard.

8. Untitled Abstract A divisibility test of arend heyting, for polynomials over a field in an intuitionistic setting In 1, arend heyting talks about polynomials over what has become known http://www.math.fau.edu/Richman/docs/heyting2.html

A division algorithm Fred Richman Florida Atlantic University Boca Raton, FL 33431 richman@fau.edu Abstract: A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitary commutative ring R , we characterize those polynomials g such that the R -module endomorphism of R X ] given by multiplication by g has a left inverse. 1 Introduction In [ ], Arend Heyting talks about polynomials over what has become known as a Heyting field ]. This is a commutative ring with an apartness relation a b , that satisfies the following properties Not a a . (consistent) If a b , then b a . (symmetric) If a b , then either a c or b c . (cotransitive) If not a b , then a b . (tight) If a b , then a c b c . (shift invariant) a if and only if a is invertible. (field) If g a a X a n X n is a polynomial with coefficients in a Heyting field, then

9. Arend Heyting Translate this page PhilSearch.de. Shops. PhiloShop. PhiloShirt. Service. Philosophie-Zitatefür Ihre HomePage. Kontakt. Impressum. eMail. arend heyting (1898 - 1980). http://www.philosophenlexikon.de/heyting.htm

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10. Philosophenlexikon.de heyting,arend; Hieronymos aus Rhodos; Hilbert, David; Hildebrand, Dietrich http://www.philosophenlexikon.de/index-hh.htm

Begriffe Abaelard - Ayer Baader - Byron Cabanis - Czezowski Ebbinghaus - Ewald ... Frauen in der Philosophie Diskussion PhilTalk Philosophieforen Andere Lexika PhilLex -Lexikon der Philosophie Lexikon der griechischen Mythologie PhiloThek Bibliothek der Klassiker Zeitschriftenlesesaal Nachschlagewerke Allgemeine Information ... Dokumentenlieferdienste Spiele Philosophisches Galgenraten PhilSearch.de Shops PhiloShop PhiloShirt Service Kontakt Impressum eMail Philosophen und Logiker [a] [b] [c] [d] ... [z] H Habrotelia von Tarent Haecker, Theodor Hahn, Hans Haldane, John Scott ... Hypatia von Alexandria powered by Uwe Wiedemann

11. Biografia De Heyting, Arend Translate this page heyting, arend. (Amsterdam, 1898-Lugano, 1980) Matemático neerlandés. Profesoren la Universidad de Amsterdam, se especializó en lógica matemática. http://www.biografiasyvidas.com/biografia/h/heyting.htm

Inicio Buscador Utilidades Recomendar sitio Enlaces Heyting, Arend (Amsterdam, 1898-Lugano, 1980) Matemático neerlandés. Profesor en la Universidad de Amsterdam, se especializó en lógica matemática. Estableció, junto con L.E.J. Brouwer, la teoría institucionalista, que rechaza el método axiomático y se orienta hacia las demostraciones de tipo intuicionista. Inicio Buscador Recomendar sitio

12. Re: Philosophy Of Math, Good Surveys? [was: Aspects Of The History Of Proofs.1/4 On Wed, 12 Feb 1997 you wrote heyting's INTUITIONISM. AN INTRODUCTION is an good Mathematics and Putting the Body back in." heyting, arend (18981980) "Intuitionism http://mathforum.com/epigone/math-history-list/shercrenflon

Re: philosophy of math, good surveys? [was: Aspects of the history of proofs.1/4] by Antreas P. Hatzipolakis reply to this message post a message on a new topic Back to math-history-list Subject: Re: philosophy of math, good surveys? [was: Aspects of the history of proofs.1/4] Author: xpolakis@hol.gr Date: http://users.hol.gr/~xpolakis/ The Math Forum

13. The Mathematics Genealogy Project - Arend Heyting arend heyting Biography Ph.D. Universiteit van Amsterdam 1925. According to ourcurrent online database, arend heyting has 8 students and 74 descendants. http://www.genealogy.ams.org/html/id.phtml?id=45623

14. Thematic Afternoon On Constructivism Thematic Afternoon on CONSTRUCTIVISM including the first arend heytingLecture Date 020 638 5606. ABOUT THE arend heyting LECTURE. The http://staff.science.uva.nl/~anne/heyting.html

15. Spreads And Choice In Constructive Mathematics definition of a tree (spread law) as heyting does, but heyting includes in a spread a complementary law which 2 heyting, arend, Intuitionism, an introduction, NorthHolland 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

16. Godel 3 Galley. Project for Ergebnisse , A proposed joint book with arend heyting (seeCorrespondence Series I heyting, arend) 11, Drafts by arend heyting http://libweb.princeton.edu/libraries/firestone/rbsc/aids/godel/godel3.html

IV. Drafts and Offprints Box/Folder AMs Notebook (in Gabelsberger shorthand) labelled "Diss. unrein," written both directions [1929?] TMs [carbon] (in German) labelled "Dissertation," with autograph corrections, 34 pp. [1929?] TMs (in German), labelled "Vollstandigkeit d. Axiome" with autograph corrections, 20 pp. [1930?] Printed page proof with autograph corrections [1930?] Offprint 1930 Galley with autograph annotations [1930] TMs (in German) with autograph corrections, pp. 10 [1930] AC describing contents of original file n.d. Erkenntnis 2 TMs [carbon] of discussion (in German) with autograph corrections, p. 23 ca.1930 TMs of Nachtrag ("Supplement"), with autograph corrections, 3 pp., back labelled "Erkenntnis" [1931?] TMs of Nachtrag with autograph corrections, p. 3 Offprint with autograph annotations [1931] Copy of Erkenntnis 2 with autograph annotations 1931 Undecidability Results (early drafts of AMs (in Gabelsberger shorthand) in 2 Notebooks, one inserted in the other, labelled "Unentsch. unrein," written both directions [1930?] AMs Notebook (in Gabelsberger shorthand), labelled "Unentsch. unrein," written both directions [1930?]

17. Godel 1 64, Herbrand, Jacques, 1931. heyting, arend 65, 19311933. 66, 1957, 1969. 32,Zentralblatt für Mathematik (re Gödel/arend heyting Collaboration) 1931-1935. http://libweb.princeton.edu/libraries/firestone/rbsc/aids/godel/godel1.html

I. Personal and Scientific Correspondence, 1929-1978 Box/Folder Addison, John Miscellaneous "A" Behman, Heinrich Bernays, Paul: [See also Series XIII: Folders 6 and 7] Boone, William: January-May, 1958 June-August, 1958 n.d. Brutian, George A. Burks, Arthur Miscellaneous "B": T. R. Bachiller to Errett Bishop Max Black to Terrell Ward Bynum Carnap, Rudolf [See also Series XIV: Folder 1] Chang, C. C. Chomsky, Noam Chuaqui Kettlun, Rolando B. 1969-1972, n.d. Church, Alonzo Cohen, Paul J.: April 24-July 17, 1963 July 20-September 27, 1963 October 4-December 13, 1963 Miscellaneous "C": Ronald Calinger to D. V. Choodnovsky Jeffrey Cohen to Haskell B. Curry Davis, Martin: 1965, n.d. Dreben, Burton S. Miscellaneous "D" [Einstein, Albert: see Miscellaneous "E"] Ellentuck, Erik: Miscellaneous "E" Feferman, Solomon: Feigl, Herbert: Fisher, Edward R., Jr. Flexner, Abraham Ford, Lester R. (re: Friedburg, Robert Friedman, Harvey: Miscellaneous "F" Gandy, R. O. Grandjean, Burke 1957-1961, includes undated notes Miscellaneous "G" Halpern, James, includes discussion notes Hasenjaeger, G.

18. Logikùv Rok Translate this page Kvìten. 5. 5. Löwenheim, Leopold, (+ 1957). 9. 5. heyting, arend, (* 1898). Èervenec.1. 7. Leibniz, Gottfried Wilhelm von, (* 1646). 9. 7. heyting, arend, (+ 1980). http://www.volny.cz/logici/vyroci/

Logikùv rok Leden Únor Bøezen Duben ... Prosinec Leden Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis Únor Russell, Bertrand Artur William Lewis, Clarence Irving Arnauld, Antoine von Neumann, Johannes Post, Emil Leon Herbrand, Jean Dedekind, Richard £ukasiewicz, Jan Hilbert, David Whitehead, Alfred North Nicod, Jean Fraenkel, Adolf Abraham Ramsey, Frank Plumpton Brouwer, Luitzgen Egbertus Jan Bøezen Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm Duben Vaught, Robert Lawson Venn, John Vaught, Robert Lawson Lewis, Clarence Irving Peirce, Charles Sanders Peano, Giuseppe Post, Emil Leon Wittgenstein, Ludwig Gödel, Kurt Wittgenstein, Ludwig Kvìten Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf Èerven Turing, Alan Mathison Church, Alonzo von Wright, Georg Henrik von Wright, Georg Henrik Turing, Alan Mathison

19. Logician's Year May. 5 May, Löwenheim, Leopold, (+ 1957). 9 May, heyting, arend, (* 1898). July.1 Jul, Leibniz, Gottfried Wilhelm von, (* 1646). 9 Jul, heyting, arend, (+ 1980). http://www.volny.cz/logici/vyroci/english.html

The Logician's Year January February March April ... December January 5 Jan Kleene, Stephen Cole 6 Jan Cantor, Georg 12 Jan Hintikka, Jaakko 14 Jan Carroll, Lewis Tarski, Alfred Gödel, Kurt 19 Jan Ramsey, Frank Plumpton 23 Jan Hilbert, David 26 Jan Kleene, Stephen Cole 27 Jan Carroll, Lewis February 2 Feb Russell, Bertrand Artur William 3 Feb Lewis, Clarence Irving 6 Feb Arnauld, Antoine 8 Feb von Neumann, Johannes 11 Feb Post, Emil Leon 12 Feb Herbrand, Jean Dedekind, Richard 13 Feb £ukasiewicz, Jan 14 Feb Hilbert, David 15 Feb Whitehead, Alfred North 16 Feb Nicod, Jean 17 Feb Fraenkel, Adolf Abraham 22 Feb Ramsey, Frank Plumpton 27 Feb Brouwer, Luitzgen Egbertus Jan March 3 Mar Cantor, Georg 5 Mar Barwise, Jon 6 Mar Davidson, Donald 7 Mar Montague, Richard 18 Mar de Morgan, Augustus Carnap Rudolf 23 Mar Skolem, Thoralf 24 Mar Lorenzen, Paul 25 Mar Ackermann, Wilhelm April 2 Apr Vaught, Robert Lawson 4 Apr Venn, John Vaught, Robert Lawson 12 Apr Lewis, Clarence Irving 19 Apr Peirce, Charles Sanders 20 Apr Peano, Giuseppe 21 Apr Post, Emil Leon 26 Apr Wittgenstein, Ludwig 28 Apr Gödel, Kurt

20. 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.

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