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         Gentzen Gerhard:     more detail
  1. The collected papers of Gerhard Gentzen (Studies in logic and the foundations of mathematics) by Gerhard Gentzen, 1969
  2. Gerhard Gentzen
  3. German Logicians: Immanuel Kant, Gottfried Leibniz, Georg Cantor, Gottlob Frege, Gerhard Gentzen, Christoph Gottfried Bardili
  4. People From the Province of Pomerania: Edward Sapir, Rudolf Virchow, Gerhard Gentzen, Carl Meinhof, Hermann Grassmann, Max Schmeling
  5. Academics of the Charles University: Albert Einstein, Jan Hus, Ernst Mach, Ewald Hering, Gerhard Gentzen, Tomás Garrigue Masaryk, Alfred Weber
  6. People From Greifswald: Caspar David Friedrich, Gerhard Gentzen, Robin Szolkowy, Hans Fallada, Magnus Von Braun, Toni Kroos, Kurt Wolff
  7. Recherches Sur La Deduction Logique by Gerhard GENTZEN, 1955
  8. Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01
  9. Die Gegenwartige Lage in der Mathematischen Grundlagenforschung [bound with] Neue Fassung des Widerspruchsfreiheitsbeweises fur die Reine Zahlentheorie. [Facsimile reprint of 1938- text in Fraktur] by Gerhard Gentzen, 1969-01-01
  10. Patrones inferenciales.: An article from: Crîtica by Axel Arturo Barcelô Aspeitia, 2008-12-01
  11. Logic's Lost Genius (History of Mathematics) by Eckart Menzler-Trott, 2007-11-21
  12. Natural Deduction: A Proof-Theoretical Study by Dag Prawitz, 2006-02-24

61. Gerhard Gentzen: Information From Answers.com
Citations The Collected Papers of gerhard gentzen Szabo ME Szabo, editor. The Collected Papers of gerhard gentzen. North-Holland, 1969.
http://www.answers.com/topic/gerhard-gentzen
showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Gerhard Gentzen Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); Gerhard Gentzen Gerhard Gentzen November 24 August 4 ) was a German mathematician and logician Born in Greifswald Germany , he died in Prague Czechoslovakia in a prisoner of war camp , after being arrested by the Russians due to his Nazi loyalties. He was one of Weyl 's students at the University of G¶ttingen from to . His main work was on the foundations of mathematics , in proof theory , specifically natural deduction and the sequent calculus . His cut-elimination theorem is the cornerstone of proof-theoretic semantics , and some philosophical remarks in his "Investigations into Logical Deduction", together with Wittgenstein's aphorism that "meaning is use", constitute the starting point for inferential role semantics
References
  • Eckart Menzler-Trott.

62. Logician's Year
+, gentzen, gerhard, (+ 1945). 6 Aug, +, Arnauld, Antoine, (+ 1694). 11 Aug, +,Church, Alonzo, (+ 1995). 27 Aug, *, Peano, Giuseppe, (* 1858)
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

63. Logikùv Rok
Translate this page Èerné pivo, gentzen, gerhard, (+ 1945). 6. 8. Èerné pivo, Arnauld, Antoine,(+ 1694) 24. 11. Svìtlé pivo, gentzen, gerhard, (* 1909)
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

64. INDEX OF NAMES
gentzen, gerhard (Germany, 19091945) and consistency of arithmetic, 1168 andtransfinite induction, 1163 Gibbs, J. Willard (USA, 1839-1903)
http://www.wolframscience.com/nksonline/index/names/f-j.html?SearchIndex=Hilbert

65. References
gentzen 69 G. gentzen. Investigations into logical deduction. In ME Szabo,editor, The collected papers of gerhard gentzen, pages 68131.
http://www.itee.uq.edu.au/~gwat/thesis/refs.html
References
Aargaard et al. 99
Mark D. Aargaard, Robert B. Jones, and Carl-Johan H. Seger. Lifted-FL: A pragmatic implementation of combined model checking and theorem proving. In Bertot et al. [ Bertot et al. 99 ], pages 323-340.
Abrial
J.-R. Abrial. Overview and rationale of an industrial prover. originally published on WWW. Informal proceedings of User Interfaces for Theorem Provers 1998. http://www.win.tue.nl/cs/ipa/uitp/proceedings.html
Abrial 96
Jean-Raymond Abrial. The B-book : assigning programs to meanings . Cambridge University Press, 1996.
Agerholm and Gordon 95
S. Agerholm and M. Gordon. Experiments with ZF set theory in HOL and Isabelle. Technical Report RS-95-37, BRICS, University of Aarhus, Denmark, 1995. http://www.brics.dk/RS/95/37/BRICS-RS-95-37.ps.gz
Agerholm 95
S. Agerholm. LCF examples in HOL. Computer Journal
Ambler et al. 77
Allen L. Ambler, Donald I. Good, James C. Brown, Wilhelm F. Burger, Richard M. Cohen, Charles G. Hoch, and Robert E. Wells. GYPSY: A language for specification and implementation of verifiable programs. ACM SIGPLAN Software Engineering Notices , 12(3):1-10, March 1977. ACM Conference on Language Design for Reliable Software.

66. The New York Review Of Books: 'A MATTER OF TEMPERAMENT'
Such results have in fact been obtained by gerhard gentzen, a fellow student ofmine 1931–33 in Göttingen, and an early leader in the deep branch of logic
http://www.nybooks.com/articles/1780
@import "/css/default.css"; Home Your account Current issue Archives ... Email to a friend Letter
'A MATTER OF TEMPERAMENT'
By Saunders Mac Lane , Reply by Freeman J. Dyson
In response to The Scientist as Rebel May 25, 1995 To the Editors In an eloquent article on "The Scientist as Rebel" [ NYR , May 25], Freeman Dyson writes of "the great mathematician David Hilbert, (who) after thirty years of high creative achievement ... walked into a blind alley of reductionism.... (He) proposed to solve the problems of mathematics by finding a general process that could decide ... (a) statement.... He called the process the Entscheidungsproblem . He dreamed of solving the Entscheidungsproblem Entscheidungsproblem as Hilbert formulated it cannot be solved." Entscheidungsproblem for a certain specific formal system (the first order predicate calculus, which covers essentially the logic of "and," "or," "not," "implies," and "there exists.") Dyson states that "he dreamed of solving the Entscheidungsproblem and thereby solving as corollaries all the famous unsolved problems of mathematics." before Entscheidungsproblem Dyson simply does not understand reductionism and the deep purposes it can serve. Hilbert was not "sterile."

67. \documentstyle{article} \title{Introducing The Hardline} \author
We follow in the wake of gentzen and Takeuti. In this talk we survey the resultsin proof Review of the book The Collected Papers of gerhard gentzen ,
http://www.amsta.leeds.ac.uk/events/logic97/abstracts/arai.txt

68. Re: Turing & Gentzen
According to Premysl Vihan The Last Months of gerhard gentzen in Prague ,Collegium Logicum (Annals of the Kurt Godel Society) Vol 1, gentzen was invited
http://bureau.philo.at/phlo/199805/msg00019.html
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According to Premysl Vihan "The Last Months of Gerhard Gentzen in Prague", Collegium Logicum (Annals of the Kurt Godel Society) Vol 1, Gentzen was invited by Hans Rohrbach to a position at the German University in Prague after habilitating as Dozent from Gottingen and release from army service in 1942. Rohrbach was head of the math institute and also worked as a ciphering officer for the Foreign Office. Gentzen was a member of the SA since 1933 (reaching the rank of Rottenfuhrer), the NSDAP since 1937, and the NSD Dozentenbund since 1941. His army rank was Obergefreiter. Partisans took him and several others to the local police station. The arrival at the station was filmed twice for some reason. I expect the film's whereabouts, like Gentzen's grave, is unknown. He did die of malnutrition, in the Karlovo namesti prison. I still don't know if Gentzen was a cipher officer.

69. M. E. Szabo: The Collected Works Of Gerhard Gentzen
The Collected Works of gerhard gentzen. NorthHolland Publishing Company, 1969.Introduction Investigations into Logical Deduction (1934)
http://www.andrew.cmu.edu/user/cebrown/notes/szabo.html
M. E. Szabo. The Collected Works of Gerhard Gentzen . North-Holland Publishing Company, 1969.
Introduction Investigations into Logical Deduction (1934) Introduction: At age 22 in 1932, Gentzen submitted the paper #1: "On the Existence of Independent Axiom Systems for Infinite Sentence Systems." He introduces a system of the propositional calculus as a sequent calculus based on Hertz's work. He modifies Hertz's "syllogism" rule to be Gentzen's "cut" rule. In this context he constructs an infinite set of sentences that has no independent set of axioms. He also shows that all "linear" sentence systems do have an independent axiomatization. Tarski introduced the semantic notion of logical consequence in 1936. Gentzen had developed this idea (for propositional logic) in #1. Gentzen's natural deduction system in #3 [1935, see below] provides a formalization of the notion of consequence in the sense first used by Bolzano (which was introduced by Bolzano over a hundred years earlier and is analogous to Tarski's notion). Gentzen studied axiom systems and axiomatic methods in order to contribute to Hilbert's program . Gentzen classifies mathematics into three levels (a classification which goes back to Weyl [1931]) based on how infinity is used: elementary number theory, analysis, general set theory. Gentzen, like the

70. Fvg:Gentzen, G.
gentzen, g. gentzen, gerhard Karl Erich (24. 11. 1909 Greifswald 4. 8. 1945 Praha).- nemecký matematik. 1944-1945 pracoval na Pražskej univerzite.
http://dent.ii.fmph.uniba.sk/~filit/fvg/gentzen_g.html
FILIT Obsah
Chronológia

Registre
... Zoznam G
Gentzen, g.
Gentzen, Gerhard Karl Erich (24. 11. 1909 Greifswald - 4. 8. 1945 Praha) nemecký matematik . 1944-1945 pracoval na Pra¾skej univerzite. Venoval sa hlavne základom matematiky a matematickej logike (Gentzenov formálny sytém).

71. Information
gentzen, gerhard 1909–1945 Tysk logiker. Geulincx, Arnold 1624–1669 Nederländskfilosof. Ghazali, Abu Hamid Mohammed ca 1058–1111 Persisk tänkare.
http://www.thephilosophynet.com/g.htm

E-post
A B C ... Z
G Gabler, Georg Andreas 1786–1853
Tysk filosof.
Tysk filosof och filosofihistoriker. Galilei, Galileo 1564–1642
Italiensk matematiker, fysiker, astronom och filosof.
Fransk filosof och politiker.
Engelsk filosof. Gassendi, Pierre 1592–1655
Fransk filosof, matematiker och naturforskare. Gehlen, Arnold 1904–1976
Tysk filosof och sociolog. Geijer, Erik Gustaf 1783–1847 Svensk författare, historiker och kompositör. Geijer, Karl Reinhold 1849–1922 Svensk filosof. Geiger, Moritz 1880–1937 Tysk filosof. Gentile, Giovanni 1875–1944 Italiensk filosof och politiker. Gentzen, Gerhard 1909–1945 Tysk logiker.

72. Biography-center - Letter G
gentzen, gerhard wwwhistory.mcs.st-and.ac.uk/~history/Mathe maticians/gentzen.html;Geoffrey of Monmouth, www.britannia.com/history/geofmon.html
http://www.biography-center.com/g.html
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73. Projekt
Translate this page Der Mathematiker und Logiker gerhard gentzen (1909–1945) hat bei seinem TodeFragmente eines Peckhaus, Volker gentzen, gerhard Karl Erich (1909-45) .
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... Lehrstuhl für Philosophie (Prof. Dr. Thiel) Transkription und Edition eines nachgelassenen Beweistheorie-Buchfragments von G. Gentzen
Literatur: V. Peckhaus, Gentzen, Routledge Encyclopedia of Philosophy (London/New York 1998), vol. 2, 23–25; C. Thiel, The remains of Gentzen's uncompleted book on foundations, Colloquium logicum 2000, TU Dresden 22.– 24.9. 2000, Abstracts. Projektleitung: Prof. Dr.

74. Golem.de - Lexikon
Translate this page Dieser Artikel basiert auf dem Artikel gerhard gentzen aus der freien Enzyklopädie ME Szabo) The Collected Papers of gerhard gentzen, Amsterdam 1969
http://lexikon.golem.de/Gerhard_Gentzen
News Forum Archiv Markt ... Impressum Lexikon-Suche Lizenz Dieser Artikel basiert auf dem Artikel Gerhard Gentzen aus der freien Enzyklopädie Wikipedia und steht unter der GNU Lizenz für freie Dokumentation . In der Wikipedia ist eine Liste der Autoren verfügbar, dort kann man den Artikel bearbeiten Letzte Meldungen FSC verbaut Opterons - CPUs werden billiger Photonische Textilien - Sofa als Display ... Originalartikel
Lexikon: Gerhard Gentzen
Gerhard Karl Erich Gentzen 24. November in Greifswald 4. August in Prag ) war ein deutscher Mathematiker und Logiker Beweistheorie . Die nachhaltige Bedeutung der von ihm entwickelten Methoden, Regeln und Strukturen zeigt sich heute vor allem in wichtigen Teilgebieten der Informatik, der Verifikation von Programmen. Dabei werden formale Beweise selbst als Programme gedeutet. Ausgehend von dem Hilbertschen Programm Widerspruchsfreiheit der Zahlentheorie . Er entwickelte als einer der ersten Hauptsatz Gentzen, der als Assistent David Hilberts . Noch in den letzten Tagen suchte er nach der Widerspruchsfreiheit der Mathematik.
Siehe auch
Werke + Literatur
  • Gerhard Gentzen: , Math. Z. 39 (1934) Nachdruck in: Karel Berka, Lothar Kreier:

75. Stefan Rabanus
Translate this page gentzen, gerhard (1934/1974) Untersuchungen über das logische Schließen.Reprograph. Nachdr. aus Mathemat. Zeitschrift 39 (1934) S. 176-210 u. 405-431.
http://staff-www.uni-marburg.de/~rabanus/text/didaktik/html/bibl_semantik.html
Semantik und Lexikologie Stefan Rabanus
Wenn zwei Jahreszahlen zusammen erscheinen - z.B. Frege, Gottlob (1892/
Dauses, August (1995): Semantik - Sprache und Denken. Stuttgart [GermBibl: 2 k / 48 g] Greimas, Algirdas Julien (1966/1971): Strukturale Semantik. Braunschweig 1971 [BiblDSA: Al 37/I] Lappin, Shalom (1996): The Handbook of Contemporary Semantic Theory. Oxford Leech, Geoffrey N. (1974): Semantics. Harmondsworth [GermBibl: 2 i / 4045] Lyons, John (1977): Semantics. Bd. 1 und 2. Cambridge Pohl, Inge (Hrsg.) (1995): Semantik von Wort, Satz und Text. Frankfurt am Main [GermBibl: 2k / 3356]
Philosophische Grundlagentexte. Formalisierte Logik. Kategorialgrammatik
Aristoteles ( Carnap, Rudolf ( 1956): Meaning and Necessity : a Study in Semantics and Modal Logic. Chicago [Bibl. Philo. III 1891 CAR/b 1947 2] Frege, Gottlob (1892/ Grice, H. Paul (1969): Utterer's Meaning and Intentions. In: The Philosophical Review 78, 147-177 Husserl, Edmund (1900/ Kripke, Saul A. (1963): Semantic Considerations on Modal Logic. In: Acta Philosophica Fennica 16, 83-94 Montague, Richard (1970/1974): English as a Formal Language. In: Montague, Richard (1974): Formal Philosophy. Selected Papers of Richard Montague. Edited and with an Introduction by Richmond H. Thomason. New Haven/London

76. Logical Consequence
gentzen, gerhard, 1969, The Collected Papers of gerhard gentzen, edited by MESzabo, Amsterdam North Holland. Restall, Greg, 2000, An Introduction to
http://plato.stanford.edu/entries/logical-consequence/
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Logical Consequence
A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument:
  • If we charge high fees for university, only the rich will enroll.
    We charge high fees for university.
    Therefore, only the rich will enroll.
  • There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid , that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments.

    77. Hilbert's Program
    English translation in gentzen (1969, 132213). gentzen, gerhard, 1969, TheCollected Papers of gerhard gentzen, Amsterdam North-Holland.
    http://plato.stanford.edu/entries/hilbert-program/
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    Hilbert's Program
    • 1. Historical development of Hilbert's Program
      1. Historical development of Hilbert's Program
      1.1 Early work on foundations
      Hilbert's work on the foundations of mathematics has its roots in his work on geometry of the 1890s, culminating in his influential textbook Foundations of Geometry ) (see 19th Century Geometry ). Hilbert believed that the proper way to develop any scientific subject rigorously required an axiomatic approach. In providing an axiomatic treatment, the theory would be developed independently of any need for intuition, and it would facilitate an analysis of the logical relationships between the basic concepts and the axioms. Of basic importance for an axiomatic treatment are, so Hilbert, investigation of the independence and, above all, of the consistency of the axioms. For the axioms of geometry, consistency can be proved by providing an interpretation of the system in the real plane, and thus, the consistency of geometry is reduced to the consistency of analysis. The foundation of analysis, of course, itself requires an axiomatization and a consistency proof. Hilbert provided such an axiomatization in (

    78. Return-Path John.Harrison-request@cl.cam.ac.uk Delivery-Date
    {\em The Collected Papers of gerhard gentzen} as ``Investigations into LogicalDeduction } @incollection{gentzeninvestigations, author = gerhard
    http://www.ftp.cl.cam.ac.uk/ftp/hvg/hol2000-archive/00xx/0045
    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:

    79. Classical Gentzen-type Methods In Propositional Many-valued Logics
    gentzen, G. Investigations into logical deduction, in The Collected Works ofGerhard gentzen (Szabo, ME ed.), North Holland, Amsterdam (1969) 68131
    http://portal.acm.org/citation.cfm?id=871478

    80. Citations Investigations Into Logical Deduction - Gentzen
    gentzen, G. Investigations into logical deduction. In The Collected Papers ofGerhard gentzen, ME Szabo, Ed. NorthHolland, 1969, pp. 68131.
    http://citeseer.ist.psu.edu/context/312/0

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