Geometry.Net - Scientists: Gentzen Gerhard

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

Extractions: 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]:-
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

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

Extractions: 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 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
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

Extractions: Strona gÅ³wna Ostatnie zmiany Edytuj Historia strony Strony specjalne Zmiana moich preferencji Obserwowane Ostatnio zmienione PrzesyÅanie plik³w Lista obrazk³w i multimedi³w Zarejestrowani uÅ¼ytkownicy Statystyka Losowa strona Porzucone artykuÅy Porzucone pliki Najpopularniejsze Najbardziej potrzebne Najkr³tsze NajdÅuÅ¼sze Nowoutworzone Wszystkie Zablokowane adresy IP Prosta administracja KsiÄÅ¼ki Wersja do druku Dyskusja Zaloguj mnie Pomoc Z Wikipedii, wolnej encyklopedii. Gerhard Gentzen 24 listopada 4 sierpnia niemiecki matematyk, zasÅuÅ¼ony w badaniach nad logikÄ i podstawami matematyki . MiaÅ duÅ¼y wpÅyw na powstanie system³w dowodzenia twierdzeÅ , tworzÄc miÄdzy innymi system sekwent³w Po zajÄciu Pragi przez wojska radzieckie zostaÅ aresztowany razem z pozostaÅymi profesorami niemieckiego uniwersytetu i po trzech miesiÄcach przebywania w tragicznych warunkach zmarÅ.
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

Extractions: 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.
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
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
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

Extractions: 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.
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
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

Extractions: 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
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

Extractions: 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
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
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

Extractions: 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]:-
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

Extractions: Ebbinghaus - Ewald ... Geschichte 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 Der Mathematiker und Logiker und das powered by Uwe Wiedemann
Philosophenlexikon.de
Friedrich von; gentzen, gerhard; Georgios Pachymeres; Gerber, Gustav;
http://www.philosophenlexikon.de/index-gg.htm

Extractions: Ebbinghaus - Ewald ... Geschichte 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] G powered by Uwe Wiedemann
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

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

Extractions: 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.
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

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

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