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Heyting Arend:     more detail

Intuitionism, An Introduction: Third Revised Edition by Arend Heyting, 2011-01-20 Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (Studies in logic and the foundations of mathematics) by Arend Heyting, 1959 Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01 Semantical Investigations in Heyting's Intuitionistic Logic (Synthese Library) by Dov M. Gabbay, 1981-03-31 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 Mathematische Grundlagenforschung Intuitionismus-Beweistheorie by A. [Arend] HEYTING, 1980

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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
   
   Extractions: 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

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
   
   Extractions: 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

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
   
   Extractions: 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
   
   Extractions: 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 745 biographies

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
   
   Extractions: 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
   
   Extractions: 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. 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

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
   
   Extractions: 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 Logiker powered by Uwe Wiedemann

10. Philosophenlexikon.de
    heyting,arend; Hieronymos aus Rhodos; Hilbert, David; Hildebrand, Dietrich  
    http://www.philosophenlexikon.de/index-hh.htm
    
    Extractions: 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 [a] [b] [c] [d] ... [z] H 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
    
    Extractions: 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

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
    
    Extractions: Boca Raton, FL 33431 21 June 2001 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. 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 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
    
    Extractions: 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
    
    Extractions: 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/
    
    Extractions: Leden Únor Bøezen Duben ... Prosinec Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis 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 Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm 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 Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf 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
    
    Extractions: January February March April ... December 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 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 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 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
    
    Extractions: 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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