Geometry.Net - Scientists: Gentzen Gerhard

Highlights In Proof Theory (ResearchIndex)
One of the main approaches that turned out to be the most useful in pursuit of thisprogram was that due to gerhard gentzen, in the 1930s, via his calculi of
http://citeseer.nj.nec.com/336722.html

Extractions: Abstract: This is a survey of some of the principal developments in proof theory from its inception in the 1920s, at the hands of David Hilbert, up to the 1960s. Hilbert's aim was to use this as a tool in his finitary consistency program to eliminate the "actual infinite" in mathematics from proofs of purely finitary statements. One of the main approaches that turned out to be the most useful in pursuit of this program was that due to Gerhard Gentzen, in the 1930s, via his calculi of "sequents"... (Update)
Citation
8 gentzen, gerhard. (1936) Die Widerspruchsfreiheit der reinen Zahlentheorie,Math. 132213, North Holland, Amsterdam, 1969. 9 gentzen, gerhard.
http://portal.acm.org/citation.cfm?id=567759&coll=portal&dl=ACM&CFID=11111111&CF
Citation
9 gentzen, G. 1969. Investigations into logical deduction. In The Collected Papersof gerhard gentzen, M. Szabo, Ed. North Holland, Amsterdam, 68131.
http://portal.acm.org/citation.cfm?id=371316.371511&coll=portal&dl=ACM&idx=J773&
WoLLIC'2000
gentzen33 gentzen, gerhard, Über das 193217, 1989. Szabo69 Szabo, ME,The Collected Papers of gerhard gentzen, North-Holland, Amsterdam, 1969.
http://www.cin.ufpe.br/~wollic/wollic2000/abstracts.html

Extractions: There is a compelling need of integration between the current tools for automation of formal reasoning and mechanization of mathematics (proof assistants and logical frameworks) and the most recent technologies for the development of web applications and electronic publishing. We explain the pivotal role that should be played by the Extensible Markup Language in this integration process, and how the many different pieces of technology under development at World Wide Web Consortium (W3C) should naturally fit together for the creation and maintenance of a virtual, distributed, hypertextual library of formal mathematical knowledge. Definability, Measure and Randomized Algorithm
Logician's Year
August. 4 Aug, Venn, John, (* 1834). gentzen, gerhard, (+ 1945). 14 Nov, Leibniz,Gottfried Wilhelm von, (+ 1716). 24 Nov, gentzen, gerhard, (* 1909). December.
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
Logikùv Rok
Translate this page Herbrand, Jean, (+ 1931). Srpen. 4. 8. Venn, John, (* 1834). gentzen, gerhard, (+1945). 6. 8. Arnauld, Antoine, (+ 1694). 11. gentzen, gerhard, (* 1909). Prosinec.2. 12.
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 Turing, Alan Mathison Quine, Willard Van Orman
Stephen Wolfram: A New Kind Of Science -- Index G-gi
shell patterns, 1012 randomness assumed in, 970 use of simple rules in, 860 Genomesas programs, 383 gentzen, gerhard (Germany, 19091945) and consistency of
http://www.wolframscience.com/nks/index/g-gi.html?SearchIndex=Geometrical substi
Stephen Wolfram: A New Kind Of Science -- Index F-j
909 and sphere packings, 985, 986 Gegenbauer, Leopold B. (Austria, 18491903) andGegenbauerC, 1091 gentzen, gerhard (Germany, 1909-1945) and consistency of
http://www.wolframscience.com/nks/index/names/f-j.html
G
Translate this page gentzen, gerhard (Allemagne, 1909-Prague, 1945) Dieudonné et al.78, Lalement 90. gentzen formalise la notion de démonstration
http://www.irisa.fr/lande/ridoux/LPAZ/node52.html

Extractions: Gentzen Gerhard (Allemagne, 1909-Prague, 1945) [ Lalement 90 ]. Gentzen formalise la notion de démonstration en la définissant comme un agencement de règles de déduction au contenu intuitif évident ( calcul des séquents ). Il peut ensuite raisonner sur la structure des démonstrations. L'une des règles de déduction, la règle de coupure, se révèle être redondante ; c'est le Hauptsatz de Gentzen. Le calcul des séquents de Gentzen, avec le théorème d'élimination des coupures, peut être vu comme le formalisme commun de la programmation logique et de la programmation fonctionnelle. Brièvement, la programmation fonctionnelle exploite l'élimination des coupures comme un mécanisme d'exécution, alors que la programmation logique exploite les règles de déduction comme règles de calcul de démonstrations sans coupure. Grammaire logique n. f. Depuis ses débuts, la programmation logique est impliquée dans l'analyse syntaxique [ Colmerauer 70 Colmerauer 78 ]. D'abord, on peut la considérer comme un sous-produit du travail de
Aberja - Philosophen - G
gentzen, gerhard - Biografie (Philosophenlexikon.de); Georgios
http://www.aberja.com/WissenschaftTechnik/Philosophie/Philosophen/Philosophen-G/
Consequently.org
2001/11/23. gerhard gentzen (19091945). gerhard gentzen brought the studyof logic to a completely new level with his work on the theory of proofs.
http://consequently.org/archive/2001/11/23

Extractions: Gerhard Gentzen (1909-1945) Gerhard Gentzen brought the study of logic to a completely new level with his work on the theory of proofs . Logicians, since Aristotle, have been interested not only in what you can prove, but also in proof itself. But somewhat suprisingly, up until Gentzen's time, no-one had a coherent story to tell about what a proof actually is and what logical properties proofs might have. Gentzen's work changed this, and he is now seen as the archetypal proof theorist Gentzen's innovation was to introduce proof as an object of study. He formalised two different kinds of proofs, which we now call Natural Deduction and Gentzen Systems in his honour. A Gentzen system is an interesting kind of way of proving things, because unlike other kinds of proof, a Gentzen proof is not a series of statements, each of which follows from earlier statements in the series. (A Natural deduction proof is like this, except that statements may be assumed and assumptions may also be discharged at different points in the proof.) A Gentzen proof is very different: at each stage of a Gentzen proof, you prove not
Index
Translate this page I Aussagenlogik Semantischer Schlussbegriff I Aussagenlogik Semantischer SchlussbegriffII Prädikatenlogik gentzen, gerhard Syntax gentzen-Kalkül see
http://logik.phl.univie.ac.at/~chris/skriptum/node78.html

Extractions: Prädikatenlogik der ersten Stufe Vorherige Seite: Sonstige zitierte Literatur Inhalt Abkürzungen Verwendete Zeichen und Abkürzungen to Einige griechische Buchstaben Ableitung Syntaktischer Schlussbegriff Ableitungsregel see Transformationsregel actual world (engl.) see tatsächliche Welt Addition Alle see Quantor Allquantor Bausteine Formationsregeln Allquantor-Beseitigung see Regel der Allquantor-Beseitigung Allquantor-Einführung see Regel der Allquantor-Einführung Alternation see Disjunktion Annahme see Regel der Annahme Antecedens Formationsregeln Argument Grundbegriffe arity (engl.)
Fußnoten
gerhard gentzen und Stanisaw
http://logik.phl.univie.ac.at/~chris/skriptum/footnode.html
Vertriebene
Translate this page Funk, Paul (1886-1969) Berichtigung, 75, 172-173 77, 164. gentzen, gerhard(1909-1945), 75, 173-174. Gödel, Kurt (1906-1978), 75, 191-192.
http://www.mathematik.uni-bielefeld.de/DMV/archiv/pinl.html

Extractions: In den Jahresberichten der DMV zwischen 1969 und 1974 hat Max Pinl unter dem obigen Titel derjenigen Fachkollegen gedacht, die durch die Unmenschlichkeit des nationalsozialistischen Regimes ihre Heimat, ihre Stellung oder gar ihr Leben verloren haben. A B C D ... Z Alt, Frank (1910-) Artin, Emil (1898-1963) Baer, Reinhold (1902-1979) Barneck, Alfred (1885-1964) Basch, Alfred (1882-1958) Baule, Bernhard (1891-1976) Behrend, Felix (1911 - 1962) Bergmann, Gustav (1906- ) Bergmann, Peter (1915- ) Bergman, Stefan (1895-1977) Bernays, Paul (1888-1977) Bernstein, Felix (1878-1956) Bers, Lipman (1914-1993) Berwald, Ludwig (1883-1942) Blumenthal, Otto (1876-1944)
Dissertationen In Mathematik, 1907-1944
Translate this page Annalen, Bd. 109, M, gentzen, gerhard, Untersuchungen über das logische Schließen.Göttingen, 02.11.1934, Grundlagen, Logik, Math. Zeitschrift, Bd. 39,
http://www.mathematik.uni-bielefeld.de/DMV/archiv/dissertationen/1934.html
Collected Works In Mathematics And Statistics
3 G38 1987, Killam. gentzen, gerhard, 19091945, The collected papersof gerhard gentzen, 1, QA 9 G329, Killam. Germain, Sophie, 1776-1831,
http://www.mathstat.dal.ca/~dilcher/collwks.html

Extractions: This is a list of Mathematics and Statistics collected works that can be found at Dalhousie University and at other Halifax universities. The vast majority of these works are located in the Killam Library on the Dalhousie campus. A guide to other locations is given at the end of this list. If a title is owned by both Dalhousie and another university, only the Dalhousie site is listed. For all locations, and for full bibliographic details, see the NOVANET library catalogue This list was compiled, and the collection is being enlarged, with the invaluable help of the Bibliography of Collected Works maintained by the Cornell University Mathematics Library. The thumbnail sketches of mathematicians were taken from the MacTutor History of Mathematics Archive at the University of St. Andrews. For correction, comments, or questions, write to Karl Dilcher ( dilcher@mscs.dal.ca You can scroll through this list, or jump to the beginning of the letter: [On to B] [Back to Top]
Www.ftp.cl.cam.ac.uk/ftp/hvg/hol2000-archive/00xx/0045
article{gentzenuntersuchungen, author = gerhard gentzen , title = Untersuchungen{{\ u}ber} das logische {Schliessen} , journal = Mathematische Zeitschrift
http://www.ftp.cl.cam.ac.uk/ftp/hvg/hol2000-archive/00xx/0045

Extractions: Return-Path: Delivery-Date: Received: from leopard.cs.byu.edu (no rfc931) by swan.cl.cam.ac.uk with SMTP (PP-6.5) outside ac.uk; Tue, 7 Jun 1994 18:53:03 +0100 Received: by leopard.cs.byu.edu (1.37.109.8/16.2) id AA01656; Tue, 7 Jun 1994 11:50:29 -0600 Sender: hol2000-request@lal.cs.byu.edu Errors-To: hol2000-request@lal.cs.byu.edu Precedence: bulk Received: from cornell.edu by leopard.cs.byu.edu with SMTP (1.37.109.8/16.2) id AA01652; Tue, 7 Jun 1994 11:50:28 -0600 Received: from msiadmin.cit.cornell.edu ([128.253.216.2]) by cornell.edu with SMTP id ; Tue, 7 Jun 1994 13:49:44 -0400 Date: Tue, 7 Jun 1994 13:49:25 -0400 From: garrel@msiadmin.cit.cornell.edu (Garrel Pottinger-MSI Visitor) Received: from msipawn.409col_ave by msiadmin.cit.cornell.edu (4.1/1.5) id AA10448; Tue, 7 Jun 94 13:49:25 EDT Message-Id:
Vrin=autres
Translate this page LARGEAULT, Jean - BERNAYS, Paul - BROUWER, Luitzen Egbertus Jan - gentzen, gerhard- GÖDEL, K. - HILBERT, David - KREISEL, Georg - WEYL, Hermann Éd.
http://www.umr8547.ens.fr/Series/Vrin=autres.html

Extractions: histoire, culture, philosophie 45 rue d'Ulm 75005 Paris Vrin (autres collections) BENZ, Ernst LES SOURCES MYSTIQUES DE LA PHILOSOPHIE ROMANTIQUE ALLEMANDE. PARIS Vrin 1987 [© 1987] 153 pp. 22,5 x 14 cm. "Vrin - Reprise" BRÉHIER, Émile - RICOeUR, Paul HISTOIRE DE LA PHILOSOPHIE ALLEMANDE. Troisième éd. avec un Appendice: "DE HUSSERL À HEIDEGGER", par P. Ricoeur. PARIS J. Vrin 1967 (© 1921 - 1954, 3e éd.) 265 pp. 19 x 14 cm. BRISSON, Luc Introduction à la Philosophie du mythe, 1. SAUVER LES MYTHES. PARIS Vrin 1996 245 pp. 21,5 x 13,5 cm. "Essais d'art et de philosophie" CASTILLO, Monique KANT. L'invention critique. PARIS Vrin 1997 247 pp. 21,5 x 13,5 cm. "Bibliothèque des philosophies" DIXSAUT, Monique Éd. CONTRE PLATON. 1. Le platonisme dévoilé. Textes réunis par M. Dixaut. PARIS Univ. de Paris XII - Vrin 1993 464 pp. 21,5 x 13,5 cm. "Tradition de la pensée classique" DIXSAUT, Monique Éd. CONTRE PLATON. 2. Renverser le platonisme. Textes réunis par M. Dixaut. PARIS Univ. de Paris XII - Vrin 1995 322 pp. 21,5 x 13,5 cm. "Tradition de la pensée classique"
ECKART MENZLER-TROTT
Translate this page gerhard gentzen (1909-1945). gentzen. Jan von Plato, gentzen und die Beweistheorie.gerhard gentzen, Drei Vorträge Der Unendlichkeitsbegriff
http://www.menzler-trott.de/d_genz_d.html

Extractions: Neben der klassischen Aufgabe einer wissenschaftlichen Autobiographie (1) galt es aber auch andere Fragen zu beantworten. Kann Naturwissenschaft allein in freien und demokratischen Gesellschaften wirklich gedeihen? Ist die Geschichte der Wissenschaft in totalitären Regimen nur eine Geschichte der Unterdrückung "guter" Wissenschaft oder eines bloßen Überlebens in mehr oder weniger unbehelligten Nischen? Wie sieht die Leistungsbilanz der reinen Mathematik, hier insbesondere der mathematischen Beweistheorie aus, wenn man die Verbrechen und Verfehlungen betrachtet, die im Namen der nationalsozialistischen Wissenschaft zustande kamen (wenn es denn eine solche Wissenschaft gab). Auch innerhalb einer Mobilisierung oder der Selbstmobilisierung der Mathematik im NS war das Hervorbringen von fachlich Neuem möglich. Das zeigt sich besonders am Werk von Gerhard Gentzen, dem größten Klassiker der mathematischen Beweistheorie. (1) Vgl. zur Bedeutung der Biographie in der Wissenschaftsgeschichte L. Pearce Williams, The Life of Science and Scientific Lives, S. 199-213, in Physis, 28 (1991)
The Mathematics Genealogy Project - Index Of GE
Translate this page Gentz, Barbara, Universität Zürich, 1996. gentzen, gerhard, Georg-August-UniversitätGöttingen, 1934. Gentzsch, Wolfgang, Technische Universität Darmstadt, 1974.
http://genealogy.math.ndsu.nodak.edu/html/letter.phtml?letter=GE&fShow=1

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