1. Gentzen Gerhard Gentzen. Born 24 Nov Gerhard Gentzen's father was a lawyerwho practiced law in Bergen on the Isle of Rügen. It was there http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Gentzen.html

Gerhard Gentzen Born: 24 Nov 1909 in Greifswald, Germany Died: 4 Aug 1945 in Prague, Czechoslovakia Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Gerhard Gentzen Gymnasium in Stralsund. Certainly moving schools did not affect Gentzen's academic achievements for when he received his Arbitur in 1928 it was with distinction and he was ranked top in his school. In [6] Robbel describes the intellectual world of the young Gentzen in particular examining the influences on him of his grandparents (especially A Bilharz) and his parents. The results of his 1928 Reifeprufung examination are given in an appendix to [6]. The headmaster of the Humanistische Gymnasium was certainly impressed with the results and, recognising his exceptional mathematical abilities, awarded him a university scholarship. Weyl for his doctorate on the foundations of mathematics. He was taught by Bernays Courant Hilbert Kneser ... Landau and, of course, his supervisor Weyl Hilbert 's assistant in 1934. M E Szabo writes in [2]:-

2. Gerhard Gentzen - Wikipedia Gerhard Gentzen. From Wikipedia, the free encyclopedia. Gerhard Gentzen (November 24, 1909 August 4, 1945) was a http://www.wikipedia.com/wiki/Gerhard_Gentzen

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Gerhard Gentzen From Wikipedia, the free encyclopedia. Gerhard Gentzen November 24 August 4 ) was a German mathematician Born in Greifswald Germany . Died in Prague Czechoslovakia , (today Czech republic He was Weyl 's student at the University of Göttingen from to . His main work was on the fundamentals of mathematics Edit this page Discuss this page Older versions ... Recent changes It was last modified 14:51 Oct 26, 2002. All text is available under the terms of the GNU Free Documentation License Main Page Recent changes Random page ... Bug reports

3. The Consistency Of Arithmetic Gen Tzen Notes prepared by March 13, 2001 The Consistency of Arithmetic gentzen gerhard Gentzen (19091945) 1934 Investigations on logical deduction. 1936 - The consistency of number theory. http://www.thoralf.uwaterloo.ca/htdocs/WWW/PDF/gentzen.pdf

4. Gerhard Gentzen - Wikipedia Gerhard Gentzen. From Wikipedia, the free encyclopedia. http://www.wikipedia.org/wiki/Gerhard_Gentzen

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Gerhard Gentzen From Wikipedia, the free encyclopedia. Gerhard Gentzen November 24 August 4 ) was a German mathematician Born in Greifswald Germany . Died in Prague Czechoslovakia , (today Czech republic He was Weyl 's student at the University of Göttingen from to . His main work was on the fundamentals of mathematics Edit this page Discuss this page Older versions ... Recent changes It was last modified 14:51 Oct 26, 2002. All text is available under the terms of the GNU Free Documentation License Main Page Recent changes Random page ... Bug reports

5. Gerhard Gentzen - Wikipedia Gerhard Gentzen. Gerhard Gentzen (24 listopada 1909 4 sierpnia 1945) - niemieckimatematyk, zasluzony w badaniach nad logika i podstawami matematyki. http://pl.wikipedia.org/wiki/Gerhard_Gentzen

Strona gł³wna Ostatnie zmiany Edytuj Historia strony Strony specjalne Zmiana moich preferencji Obserwowane Ostatnio zmienione Przesyłanie plik³w Lista obrazk³w i multimedi³w Zarejestrowani użytkownicy Statystyka Losowa strona Porzucone artykuły Porzucone pliki Najpopularniejsze Najbardziej potrzebne Najkr³tsze Najdłuższe Nowoutworzone Wszystkie Zablokowane adresy IP Prosta administracja KsiÄ Å¼ki Wersja do druku Dyskusja Zaloguj mnie Pomoc Gerhard Gentzen Z Wikipedii, wolnej encyklopedii. Gerhard Gentzen 24 listopada 4 sierpnia niemiecki matematyk, zasłużony w badaniach nad logikÄ i podstawami matematyki . Miał duży wpływ na powstanie system³w dowodzenia twierdzeń , tworzÄ c między innymi system sekwent³w Po zajęciu Pragi przez wojska radzieckie został aresztowany razem z pozostałymi profesorami niemieckiego uniwersytetu i po trzech miesiÄ cach przebywania w tragicznych warunkach zmarł. Edytuj Dyskusja Historia strony LinkujÄ ce ... Ostatnie zmiany Tę stronę obejrzano 23 razy; ostatnio zmodyfikowano o 11:05, 22 lis 2002; udostępniana jest w oparciu o licencję GNU FDL Strona gł³wna Ostatnie zmiany Losuj stronę ... Raport o błędach

6. Gerhard Gentzen Gerhard Karl Erich Gentzen. Gerhard Karl Erich Gentzen absolvoval gymnáziumve Stralsundu a poté studoval dva semestry na univerzite vGöttingen. http://www.math.muni.cz/math/biografie/gerhard_gentzen.html

Gerhard Karl Erich Gentzen Narozen: 24. listopadu 1909 v Greifswaldu Zemøel: 4. srpna 1945 v Praze Gerhard Karl Erich Gentzen absolvoval gymnázium ve Stralsundu a poté studoval dva semestry na univerzitì v G öttingen. Dále studoval po jednom semestru na univerzitách v Mnichovì a v Berlínì. Pak se vrátil zpìt do Göttingen, kde v roce 1933 získal doktorát za práci Untersuchungen über das logische Schliessen. Ve stejném roce se stal asistentem D. Hilberta. V roce 1940 se habilitoval s prací Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie. Roku 1943 byl jmenován mimoøádným profesorem na nìmecké univerzitì v Praze, kde pùsobil do kvìtna roku 1945. Ve své práci se Gerhard Karl Erich Gentzen zabýval logikou a základy matematiky. Literatura: Pinl, M.: Kollegen in einer dunklen Zeit. Jahresbericht der Deutschen Mathematiker-Vereinigung. 75 (1974), str.173-174. Autor: Jaroslav Folta, Pavel ©i¹ma

7. Gerhard Gentzen - Acapedia - Free Knowledge, For All Friends of Acapedia Gerhard Gentzen. From Wikipedia, the free encyclopedia. GerhardGentzen (November 24, 1909 August 4, 1945) was a German mathematician. http://acapedia.org/aca/Gerhard_Gentzen

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8. Lukax - Matematika Na Internetu algebry. Gauss Carl Friedrich Viz Osobnosti Karl Gauss gentzen gerhardKarl Erich Narozen 24. listopadu 1909, zemrel 4. srpna 1945. http://www.czech-ware.net/lukax/osob/g.asp

9. Classmark Author Title Item Status Barcode Serials (item Status QA9 GEN, gentzen gerhard 19091945, Collected papers, 01, 1500442007. GC190GIL, Gill Adrian E. Atmosphere-ocean dynamics Adrian E. Gill, 01, 1500085461. http://www.maths.bris.ac.uk/~amnag/library/mathsclass.htm

Classmark Author Title Item status Barcode Serials (item status 57 = Holdings record) Unclassified Fundamenta mathematicae Proceedings of symposia in pure mathematics Stack 1400 American Mathematical Society translations Annual review of fluid mechanics Annual review of fluid mechanics Annual review of fluid mechanics Annual review of fluid mechanics Books ABL Ablowitz Mark J. Solitons and the inverse scattering transform Mark J. Ablowitz and Harvey Segur ACH Acheson D.J. Elementary fluid dynamics D.J. Acheson AB Ackermann W. Wilhelm Solvable cases of the decision problem by W. Ackermann AIN Ainley Stephen Mathematical puzzles Stephen Ainley AND Anderson John D. John David Fundamentals of aerodynamics John D. Anderson, Jr. AND Anderson John D. John David 1930- Fundamentals of aerodynamics John D. Anderson, Jr APE Apel John R. John Ralph 1930- Principles of ocean physics John R. Apel ARI Aris Rutherford Vectors, tensors, and the basic equations of fluid mechanics Rutherford Aris ATH Athreya K.B. Krishna B.

10. Virtual Encyclopedia Of Mathematics pierre gauss carl friedrich gegenbauer leopold geiser karl friedrich gelfond aleksandrosipovich gellibrand henry geminus gentzen gerhard gergonne joseph diaz http://www.lacim.uqam.ca/~plouffe/Simon/supermath.html

Super-Index of Biographies of Mathematicians abel niels henrik abraham bar hiyya ha-nasi abraham max abu kamil shuja ibn aslam ibn muhammad ... zygmund antoni This index was automatically generated using a new tagging program written by Simon Plouffe at LaCIM

11. References For Gentzen References for gerhard gentzen. Biography Books ME Szabo (ed.), Collectedpapers of gerhard gentzen, Studies in Logic (Amsterdam, 1969). Articles http://www-gap.dcs.st-and.ac.uk/~history/References/Gentzen.html

References for Gerhard Gentzen Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: M E Szabo (ed.), Collected papers of Gerhard Gentzen, Studies in Logic (Amsterdam, 1969). Articles: A Indrzejczak, Jaskowski and Gentzen approaches to natural deduction and related systems, in The Lvov-Warsaw School and Contemporary Philosophy 1995 (Dordrecht, 1998), 253-264. P Pudlak, A foreword to the translation of G Gentzen's paper : "The current state of research in the foundations of mathematics" (Czech), Pokroky Mat. Fyz. Astronom. A R Raggio, The 50th anniversary of Gentzen's thesis, in Methods and applications of mathematical logic, Campinas, 1985 (Providence, RI, 1988), 93-97. G Robbel, Aus der Gedankenwelt des jungen Gerhard Gentzen, Humboldt Univ. Ber. P Vihan, The last months of Gerhard Gentzen in Prague, Collegium logicum Vol. 1 (Vienna, 1995), 1-7. P Vihan, Gerhard Gentzen (1909-1945) (Czech), Pokroky Mat. Fyz. Astronom. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR September 2001 School of Mathematics and Statistics University of St Andrews, Scotland

12. M. E. Szabo: The Collected Works Of Gerhard Gentzen ME Szabo. The Collected Works of gerhard gentzen. NorthHolland PublishingCompany, 1969. Introduction. Investigations into Logical Deduction (1934). http://www.andrew.cmu.edu/~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

13. Fvg:Gentzen, G. Chronológia Registre Diskusia Správa Zoznam G gentzen, g. gentzen, gerhard Karl Erich (24. 11. 1909 Greifswald 4. 8. 1945 Praha) - nemecký matematik. 1944-1945 pracoval na Praskej univerzite. http://www.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).

14. Gentzen Biography of gerhard gentzen (19091945) gerhard gentzen. Born 24 Nov 1909 in Greifswald, Germany http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Gentzen.html

Gerhard Gentzen Born: 24 Nov 1909 in Greifswald, Germany Died: 4 Aug 1945 in Prague, Czechoslovakia Click the picture above to see a larger version Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Gerhard Gentzen Gymnasium in Stralsund. Certainly moving schools did not affect Gentzen's academic achievements for when he received his Arbitur in 1928 it was with distinction and he was ranked top in his school. In [6] Robbel describes the intellectual world of the young Gentzen in particular examining the influences on him of his grandparents (especially A Bilharz) and his parents. The results of his 1928 Reifeprufung examination are given in an appendix to [6]. The headmaster of the Humanistische Gymnasium was certainly impressed with the results and, recognising his exceptional mathematical abilities, awarded him a university scholarship. Weyl for his doctorate on the foundations of mathematics. He was taught by Bernays Courant Hilbert Kneser ... Landau and, of course, his supervisor Weyl Hilbert 's assistant in 1934. M E Szabo writes in [2]:-

15. Gerhard Gentzen Translate this page eMail. gerhard gentzen (1909 - 1945). Der Mathematiker und Logiker gerhard gentzenbeschäftigte sich vor allem mit Problemen des logischen Schließens. http://www.philosophenlexikon.de/gentzen.htm

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16. Philosophenlexikon.de Friedrich von; gentzen, gerhard; Georgios Pachymeres; Gerber, Gustav; http://www.philosophenlexikon.de/index-gg.htm

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17. Logic The Collected Works of gerhard gentzen contains a historical account of gentzen'swork along with his papers (including his paper on cutelimination). http://www.andrew.cmu.edu/~cebrown/logic.html

Notes on Automated Theorem Proving History von Heijenoort From Frege to Godel is a collection of early papers on logic. The Collected Works of Gerhard Gentzen contains a historical account of Gentzen's work along with his papers (including his paper on cut-elimination Basic Logic Ebbinghaus, Flum, Thomas argue that first order logic is the best possible logic. Andrews builds up from propositional and first order logic to higher order logic. Type Theory Russell created Ramified Type Theory and Wiener simplified it by reducing relations to predicates. In 1940, Church introduced his type theory based on simply typed lambda calculus. Andrews proved cut elimination for a sublogic of Church's Type Theory called Elementary Type Theory Andrews' book studies Church's Type Theory in the formulation Q_0. Miller extended Herbrand's Theorem to Elementary Type Theory using expansion trees Leivant surveys results in higher order logic using Schutte's relational formulation (using comprehension instead of lambda calculus). Lambda Calculus Barendregt is the standard reference for the untyped lambda calculus.

18. WoLLIC'2000 - Proceedings Mathematical Society, 1988. gentzen33 gentzen, gerhard, Über das Verhältnis zwischen intuitionistischer und http://www.di.ufpe.br/~wollic/wollic2000/proceedings

WoLLIC'2000 th Workshop on Logic, Language, Information and Computation August 15-18, 2000 Hotel Barreira Roxa Natal Brazil Scientific Sponsorship Interest Group in Pure and Applied Logics ( IGPL European Association for Logic, Language and Information ( FoLLI Association for Symbolic Logic ( ASL SBC SBL Funding FUNPEC PROEX-UFRN Organisation CIn-UFPE DIMAP-UFRN Proceedings ( whole gzipped ps-file (500K) Invited Papers Contributed Papers Invited Papers Some Applications of Explicit Provability by Sergei Artemov (Moscow University, Russia, and Cornell University, USA) Within explicit tradition in logic (Skolem, Herbrand, Henkin, Kowalski, and others) quantifiers are replaced by functions. This makes a difference in proof theory: the desired reflection principle ``there exists a proof of F '' -> F is not provable, unlike its explicit version ``p is a proof of F'' -> F. Lambda-calculus has been enhanced to capture types depending on terms, like $t:(s:F)$ preserving strong normalization, confluence properties, and the Curry-Howard semantics of terms as proofs. New logics of knowledge with justifications opened up a possibility to tackle the well known question of how to express a fact that a derivable proposition does not have short proofs.

19. Citations: The Collected Papers Of Gerhard Gentzen - Szabo (ResearchIndex) Retrieving documents ME Szabo, The Collected Papers of gerhard gentzen, NorthHolland,Amsterdam (1969). ME Szabo. The Collected papers of gerhard gentzen. http://citeseer.nj.nec.com/context/20088/0

32 citations found. Retrieving documents... M.E. Szabo, The Collected Papers of Gerhard Gentzen , North-Holland, Amsterdam (1969). Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: Curry-Howard terms for Linear Logic - Albrecht, Bäuerle, Crossley, Jeavons (1994) (1 citation) (Correct) ....in a natural deduction proof system for intuitionistic logic. The terms, which we call Curry Howard terms, give an explicit representation of the whole proof which can be readily handled by the machine in contast to the traditional representations by mathematicians (see e.g. Gentzen s work in ) where, in discussing the manipulation of proofs, large parts are simply represented by Delta Delta Delta, and it is left to the reader to determine precisely what the Delta Delta Delta means. In the traditional situation the manipulations could be effected without too much difficulty. In ....of terms within terms. 1. In our view, Curry Howard terms provide an explicit notation for proofs. They are explicit in the sense that, given a Curry Howard term, one can write down the corresponding proof and vice versa.

20. Solomon F Eferman that due to gerhard gentzen in the http://math.stanford.edu/~feferman/papers/highlights.pdf

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