61. Liste Alphabétique Des Mathématiciens Translate this page 1968). Geminus de Rhodes, Grec (~1 er siècle). gentzen (gerhard), Allemand(1909-1945). Gérard de Crémone, Italien (v.1114-1187). Gerbert http://www.cegep-st-laurent.qc.ca/depar/maths/noms.htm

Abel (Niels Henrik) Agnesi (Maria Guetana) Italienne (1718-1799) Alembert (Jean Le Rond d') Alexander (James Waddell) Alexandroff (Pavel Sergeevich) Russe (1896-1982) Apian (Peter Benneuwitz, dit) Allemand (1495-1552) Apollonios de Perga Grec(v.~262-v.~180) Appel (Paul) Grec (~287-~212) Aristote Grec (~384-~322) Arzela (Cesare) Italien (1847-1912) Ascoli (Guilio) Italien (1843-1896) Babbage (Charles) Anglais (1792-1871) Banach (Stefan) Polonais (1892-1945) Argand (Jean Robert) Suisse (1768-1822) Barrow (Isaac) Anglais (1630-1677) Bayes (Thomas) Anglais (1702-1761) Bellavitis (Giusto) Italien (1803-1880) Beltrami (Eugenio) Italien (1835-1900) Bernays (Paul) Suisse (1888-1977) Bernoulli (Daniel) Suisse (1700-1782) Bernoulli (Jacques) Suisse (1654-1705) Bernoulli (Jean) Suisse (1667-1748) Allemand (1878-1956) Bernstein (Sergei Natanovich) Russe (1880-1968) Bertrand (Josepn) Bessel (Friedrich) Allemand (1784-1846) Birkoff (George David) Bliss (Gilbert Ames) Bochner (Salomon) Allemand (1899-1982) Bolyai (Janos) Hongrois (1802-1860) Bolzano (Bernhard) Bombelli (Raffaele) Italien (1522-1572) Bonnet (Ossian) Boole (George) Anglais (1815-1864) Bourbaki (Nicolas) Braikenridge (William) Anglais (v.1700-1762)

62. COMPUTATIONAL LOGIC:   F O R   C U R R E N T   S T U D E N T S G. gentzen. Investigations into logical deduction. In The Collected Papersof gerhard gentzen, ME Szabo, Ed. NorthHolland, 1969, pp. 68131. http://pikas.inf.tu-dresden.de/compulog/lectures/summer00/ds.html

For Current Students Deduction Systems First Part: Introduction to Proof Theory ELECTRIC LAMPS WERE NOT INVENTED BY IMPROVING CANDLES lecturer: Alessio Guglielmi The first part of the course will last three weeks, until Easter. It serves two purposes: 1) introducing Gentzen's calculus of sequents, that will be used later in the "Deduction Systems" course, and 2) providing a general overview of proof theory, especially for the students wishing to attend the seminar "Selected Topics in Proof Theory." Gentzen's Sequent Calculus will be introduced in both intuitionistic and classical variants. As an application, the main ideas underlying uniform proofs and abstract logic programming will be shown. Then, the cut-elimination theorem in Tait-Girard style will be proven. If time permits, the relation between sequent calculus and natural deduction will be shown. Lectures and tutorials will be freely intermixed in this part of the course. Students will be asked to turn in two or three homework exercises. material: We will essentially follow parts of the paper: J. Gallier.

63. Logic is currently a mix of all kind of people ) Historical logiciansGottlob Frege; Robin Gandy; gerhard gentzen; Stephen Cole Kleene; http://www.loria.fr/~roegel/cours/logic.html

Logic Here are a few interesting bookmarks on logic. (They need to be better organized, I know...) Logic (generalities) Glossary of First-Order Logic Logical fallacies Logic Logic ... Comments on various books and articles (local copy here Foundations and history of mathematics Historia-Matematica mailing list Historia-Matematica journal Foundations of Mathematics mailing list Foundations of Mathematics ... Mathematical logic and foundations Logic courses at other universities Intermediate Logic (Berkeley University, Professor Paolo Mancosu) Introduction to Mathematical Logic (Vanderbilt University) Symbolic Logic (Earlham College) Logic course at Harvey Mudd college, California Introduction course Informal logic course An elementary logic course I gave at the ESSTIN engineer school in Nancy in 1995. There were 16 hours of class. PDF file (in french) Book on philosophical logic Logic and Education Semantics La logique classique (in French, propositional calculus in Polish notation (in French, predicate calculus)

64. Bibliography 4 gerhard gentzen. Investigations into logical deduction. In M. E. Szabo, editor,The collected papers of gerhard gentzen, pages 68131. North-Holland, 1969. http://www.cs.uwyo.edu/~jlc/prop_gloss/node26.html

Next: About this document ... Up: Classical Propositional Decidability via Previous: Applications Bibliography Robert L. Constable and Douglas J. Howe. Implementing metamathematics as an approach to automatic theorem proving. In R.B. Banerji, editor, Formal Techniques in Artificial Intelligence: A Source Book , pages 45-76. Elsevier Science Publishers (North-Holland), 1990. J. H. Gallier. Logic for Computer Science: Founations of Automatic Theorem Proving Harper and Row, 1986. J. H. Gallier. Logic for Computer Science, Foundations of Automatic Theorem Proving Harper and Row, NY, 1986. Gerhard Gentzen. Investigations into logical deduction. In M. E. Szabo, editor, The collected papers of Gerhard Gentzen , pages 68-131. North-Holland, 1969. Originaly published 1935. Stephen C. Kleene. Introduction to Metamathematics van Nostrand, Princeton, 1952. Elliott Mendelson. Introduction to Mathematical Logic D. Van Nostrand, second edition, 1979. A. Nerode and R. Shore. Logic for Applications Springer-Verlag, New York, 1994. Raymond M. Smullyan.

65. Proof Technology The notion of proof we use traces its historical roots to the seminal workof gerhard gentzen on Natural Deduction (ND) and Sequent Calculi. http://www.cs.cornell.edu/Info/Projects/NuPrl/Intro/ProofTech/technology.html

Proof Technology Context Nuprl is a proof development system. Much of our effort has gone into a technology for creating and displaying proofs. When we talk about proofs in our writing, we generally mean formal proofs. This is especially true under this heading of proof technology. While the idea of a proof in the sense discovered by the Greeks and used centrally in mathematics since then is widely used, the technical notion of proof that we have in mind is relatively new, since the 1970s, and much of our technical work has contributed to creating a new notion of formal proof, one that incorporates computer programs (called tactics) to fill in details, and one that allows computers to carry out various kinds of steps such as calculation, symbolic evaluation and rewriting of one term to another. The central new idea that we introduced is called a tactic-tree proof. It built on and extended the idea pioneered in the Edinburgh LCF system of a tactic. The underlying basis of tactic-tree proofs is the notion of a sequent. Gentzen introduced sequent based proof systems, his L-systems . But we wanted to present proofs in a top-down refinement style rather than Gentzen's bottom-up style. This led us to presentations of sequent proofs in the style of Beth's tableaux . Following Bates , we call this top down sequent logic a Refinement Logic (RL) Technical Results Our first writing on Refinement Logics is Joe Bate's thesis . This is also the primitive logic of the article Proofs as Programs . The idea is that proofs are interactively built by refining a single goal into subgoals using an inference rule.

66. 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://www.stefan.rabanus.com/seminare/semantik/bibl_semantik.html

Stefan Rabanus Bibliographie zu Semantik und Lexikologie 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

67. CONSTRUCTIVISME We gaan verder met de (vrije) vertaling van een aantal Engelstalige artikelen, geschrevendoor een respectabel Duits mathematicus gerhard gentzen 15 Beter http://huizen.dto.tudelft.nl/deBruijn/gentzen.htm

CONSTRUCTIVISME Het wordt de hoogste tijd een echte wiskundige, uitgebreid, aan het woord te laten. We gaan verder met de (vrije) vertaling van een aantal Engelstalige artikelen, geschreven door een respectabel Duits mathematicus: Gerhard Gentzen Beter dan ik het zelf zou kunnen, verhaalt hij over recentere ontwikkelingen binnen de wiskunde. Het gaat om de eerste helft van de 20ste eeuw. De titel van het eerste artikel is: "Het oneindigheidsbegrip in de wiskunde", en is vrijwel integraal opgenomen. Het tweede draagt als titel: "De huidige stand van het onderzoek naar de grondslagen van de wiskunde". Verschillende gedeelten hiervan zijn weggelaten of vervangen, deels om allerlei herhalingen te vermijden, deels vanwege elementen in het oorspronkelijke artikel die in het onderhavige verband als storend worden ervaren. Gentzen's betoog bereikt een climax in het hoofdstuk getiteld: "De mogelijkheid om de verschillende gezichtspunten met elkaar te verzoenen". Aan het woord is Gerhard Gentzen: Het oneindige De analyse Verzoeningspoging Lang leve Plato

68. Literatur Zur Logik Translate this page gerhard gentzen. Untersuchungen über das logische Schließen. ME Szabo (Hrsg.).The Collected Papers of gerhard gentzen. North-Holland, 1969. Dag Prawitz. http://wwwbrauer.in.tum.de/lehre/logik/SS98/literatur.html

Weitere Literaturhinweise H.-D. Ebbinghaus, J. Flum, W. Thomas. . BI, 1992. Dirk van Dalen. Logic and Structure . Springer, 1994. (3rd edition) Herbert B. Enderton. A Mathematical Introduction to Logic . Academic Press, 1972. Stephen C. Kleene. Mathematical Logic . John Wiley, 1967. Mit Ausnahme von Logic and Structure Raymond Smullyan. First-Order Logic . Springer, 1968. Rolf Socher-Ambrosius. Deductionssysteme . BI, 1997. Rolf Socher-Ambrosius, Patricia Johann. Deduction Systems . Springer, 1997. Jean Gallier. Logic for Computer Science A. Troelstra, H. Schwichtenberg. Basic Proof Theory . Cambridge University Press, 1996. Gerhard Gentzen. . Mathematische Zeitschrift 39, (1935), S. 176-210, 405-431. M.E. Szabo (Hrsg.). The Collected Papers of Gerhard Gentzen . North-Holland, 1969. Dag Prawitz. Natural Deduction Speziell zur Aussagenlogik: Aussagenlogik: Deduktion und Algorithmen . Teubner, 1994.

69. Yamada gentzen, gerhard. Untersuchungen uber das logische Schliessen. Gottingen , UniversitatGottingen, 1933. 62 p. 21 cm. (Mathematische Zeit schrift, 39) 710-317. http://www.lib.hit-u.ac.jp/service/bunko/yamada.htm

ŽR“c‹Ôˆê•¶ŒÉ–Ú˜^ ‚P‚X‚W‚P”N‚QŒŽ‚P‚T“ú”­s §186“Œ‹ž“s‘—§Žs’†2-1 TEL(0425)72-1101 ƒRƒƒj[ˆóü TEL(0423)94-1111 ¼@â@˜a@•v ŽR“c‹Ôˆêæ¶i1906-1974j‚ÌŽv‚¢o ˆé@–ì@@C @ÅŒã‚ɁCæ¶‚̏Š‘ ‘‚ð¬•½•ªŠÙ‚ÉŠñ‘¡‚³‚ꂽŒäˆâ‘°‚ƁC“úí‹Æ–±‘½–Z‚Ì‚È‚© ‚ð‚Æ‚­‚É‚±‚Ì•¶ŒÉ‚̐®—‚Ì‚½‚ß‚É“w—Í‚³‚ꂽŠÖŒWŽÒ‚Ì•ûX‚ÉŒú‚­Š´ŽÓ‚µ‚½‚¢B (1980E12E16j @1D‚±‚Ì•¶ŒÉ‚Ì•ª—ނ́CŽR“c‹Ôˆê‹³ŽöŽ©‚炪•ª—Þ‚µ‚½‚à‚Ì‚ðC‚»‚Ì‚Ü‚Ü“¥P‚µ‚Ä ‚¢‚éB @2DŠeX‚Ì•ª—Þ‚Ì’†‚́C—m‘‚Í’˜ŽÒ–¼i•ÒŽÒ–¼jC˜a‘‚͏‘–¼‚̃Aƒ‹ƒtƒ@ƒxƒbƒg ‡‚É”r—ñ‚µ‚Ä‚ ‚éB @3D‘ΏƎ–€iƒy[ƒW”E‘å‚«‚³“™j‚Ì‚ ‚Ƃɂ́C¬•½•ªŠÙ‚É‚¨‚¯‚鐿‹‹L†‚ª ‚‚¯‚ç‚ê‚Ä‚¢‚éB @4Dõˆø‚͐l–¼õˆøiŠÜC’c‘Ì–¼j‚̂ݍ쐬‚µ‚Ä‚ ‚éB @@AD—m‘‚Ì•” @@@1DAlgebra @@@2DLogic @@@3DMathematics @@@4DStatistics ... @@@8DMiscellanea @@BD˜a‘‚Ì•” @@@1D‘㐔 @@@2D˜_— @@@3D”Šw @@@4D“Œv ... @@@8D‚»‚Ì‘¼ @@CDŽGŽ‚Ì•” @@@1D—mŽGŽ @@@2D˜aŽGŽ —m‘‚Ì•” 1. Algebra. Aitken, Alexander Craig. @@Determinants and matrices. 8. ed. @Edinburgh, Oliver and Boyd, 1954. @@vii,144 p. 19 cm. (University @mathematical texts)@@710-236 Albert, A. Adrian.

70. Qi And Sequent Notation gerhard gentzen (19091945). The use of sequent notation derives from gerhardgentzen who developed the sequent calculus treatment of first-order logic. http://www.simulys.com/qiml.htm

How is Qi different from ML? In several ways. First Qi is very well integrated into Lisp, allowing you to draw upon the full power of the Lisp environment. Second Qi allows static typechecking but does not insist on it. This means that useful constructions in Common Lisp that are not within the scope of typechecking - including macros and other devices - can be used within Qi Third Qi allows you to extend the type system to incorporate any typable aspect of Lisp or any typable Lisp package including CLOS and CLIM according to your desire Fourth and finally Qi is a deductively typed language. Types are specified in sequent rules and these rules are compiled into machine code for fast inferencing. This allows types to be defined that are beyond the capacity of ML and related languages to support. Gerhard Gentzen (1909-1945) The use of sequent notation derives from Gerhard Gentzen who developed the sequent calculus treatment of first-order logic. In Gerhard's system a

71. PMFA Matematika A Informatika 37 (1992), 185205; Premysl Vihan gerhard gentzen (1909-1945). 37 (1992),249-257; gerhard gentzen Soucasný stav ve výzkumu základu matematiky. http://mat.fsv.cvut.cz/ppjcmf/rejstrikPMFA/cl01-ma.html

Souhrnný rejstøík èlánkù z èasopisu Pokroky matematiky, fyziky a astronomie z let 1986-2000 Matematika a informatika Fyzika Astronomie Diskuse ... Rùzné Matematika a informatika Jaroslav Nešetøil: Historická perspektiva koneèné matematiky. Alica Kelemenová, Jozef Kelemen: O biológii, matematike a výpoètoch - rozhovor s A. Lindenmayerom. Petr Jirkù: Expertní systémy. Christian Pommerenke: Bieberbachova domnìnka. Petr Mandl: K tradicím a perspektivám teorie pravdìpodobnosti a matematické statistiky. John W. Dawson ml.: Zaostøeno na Kurta Gödela. S. G. Gindikin: Joseph Louis Lagrange (1736-1813). Štefan Schwarz: Preèo a ako zvyšova matematickú kultúru. Jan Polášek: Pováleèný rozvoj a perspektivy aplikované matematiky. Èást 1. Rozvoj aplikované matematiky v ÈSR ve strojírenských oborech. Karel Rektorys: Pováleèný rozvoj a perspektivy aplikované matematiky. Èást 2. O hlavním úkolu SPZV "Metody aplikované matematiky v inženýrských problémech". Stephen A. Cook: Preh¾ad teórie výpoètovej zložitosti. Karel Drbohlav: Algebra, logika a teorie množin.

72. Earliest Uses Of Symbols Of Set Theory And Logic According to MJ Cresswell and Irving H. Anellis, the upsidedown A originatedin gerhard gentzen, Untersuchungen ueber das logische Schliessen, Math. http://members.aol.com/jeff570/set.html

Earliest Uses of Symbols of Set Theory and Logic Last updated: Oct. 18, 2002 Intersection and union. Giuseppe Peano (1858-1932) introduced and in 1888 in Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann (Cajori vol. 2, page 298). According to Schwartzman (p. 118) the intersection symbol above dates back to Leibniz "who also used it to indicate regular multiplication." Cajori says Leibniz used the symbol for multiplication, but seems not to confirm that he used it for intersection. Existence. Peano used in volume II, number 1, of his which was published in 1897 (Cajori vol. 2, page 300). Membership. Peano used in the introduction to volume I of his which was published in Turin in 1895, although the introduction itself is dated 1894 (Cajori vol. 2, page 300). The website at the University of St. Andrews states that Peano introduced the symbol in 1889 and that it comes from the first letter if the Greek word meaning "is." Peano's symbol for membership was an ordinary epsilon ; the stylized epsilon now used was adopted by Bertrand Russell in Principles of Mathematics Such that.

73. Luftwaffe "Aces" gentzen, Hannes,18. gerhard, Dieter, 8. Gerth, Werner, 13. Gienanth, Eugene von, 10. Glunz,Adolf, 71. http://members.aol.com/dheitm8612/expert1.htm

Luftwaffe "Aces" The following is a partial list of Luftwaffe "aces" (using the Allied standard of 5 kills) that mostly flew Messerschmitts during their careers. Scoring five kills under the German system did not garner one the German title of " Experte ". The title was conferred on those that only exihibited consistent excellence and leadership in combat and in which the tally of victories played a minor part. For example, a German pilot may not have been considered an "Experte" until he scored his 60th victory or more. The list is ordered from left to right alphabetically by last names, first names, and victory tally (" abschuss " or " endgueltige Vernichtung "; not award points A B C ... Z Adam, Heinz-Guenther Adameit, Horst Adolph, Walter Ahnert, Heinz-Wilhelm Ahrens, Peter Aistleitner, Johann Andel, Peter Babenz, Emil Bachnick, Herbert Badum, Johann Baer, Heinrich "Heinz" Balthasar, Wilhelm Bareuter, Herbert Barkhorn, Gerhard Bartels, Heinrich Barten, Franz Bartz, Erich Batz, Wilhelm Bauer, Konrad Bauer, Viktor Becker, Paul Beckh, Friedrich

74. OPE-MAT - Historique Translate this page Marcel Fraenkel, Adolf Gellibrand, Henry Guccia, Giovanni Francais, Francais GeminusGudermann, Christoph Francais, Jacques gentzen, gerhard Guldin, Paul http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm

A Abel , Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali B Babbage , Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl

75. REP A-Z List will Generalized continuum hypothesis Genetic modification Genetics Genetics andethics Gentile, Giovanni gentzen, gerhard Karl Erich Geology, philosophy of http://www.rep.routledge.com/atoz/article/G.html

Gadamer, Hans-Georg Gaius Galen Galilei, Galileo Gandhi, Mohandas Karamchand Gardens, aesthetics of Gassendi, Pierre Gehlen, Arnold Gender and science Genealogy General relativity, philosophical responses to General will Generalized continuum hypothesis Genetic modification Genetics Genetics and ethics Gentile, Giovanni Gentzen, Gerhard Karl Erich Geology, philosophy of Geometry, philosophical issues in George of Trebizond Gerard, Alexander Gerard of Cremona Gerard of Odo Gerbert of Aurillac Gerdil, Giancinto Sigismondo German idealism Gerson, Jean Gersonides Gestalt psychology Gettier problems Geulincx, Arnold al-Ghazali, Abu Hamid Gilbert of Poitiers Giles of Rome Gioberti, Vincenzo Glanvill, Joseph Globalization Gnosticism God, arguments for the existence of God, concepts of God, Indian conceptions of Godfrey of Fontaines Godwin, William Goethe, Johann Wolfgang von Good, theories of the Goodman, Nelson Goodness, perfect Gorgias Grace Gramsci, Antonio Greatest lower bound Greatest ordinal, paradox of the Greek philosophy: impact on Islamic philosophy Green political philosophy Green, Thomas Hill

76. Biography-center - Letter G Gentry, Ruth www.agnesscott.edu/lriddle/women/gentry.htm; gentzen, Gerhardwwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/gentzen.html; http://www.biography-center.com/g.html

Visit a 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 G 523 biographies www.pathfinder.com/time/time100/scientist/profile/godel.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Godel.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Gopel.html G.i., American www.pathfinder.com/time/time100/heroes/profile/gi01.html Gabbiani, Beppe www.grandprix.com/gpe/drv-gabbep.html Gabelich, Gary www.hickoksports.com/biograph/gabelichg.shtml Gable, Daniel M. www.hickoksports.com/biograph/gabledan.shtml Gabor, Dennis www.nobel.se/physics/laureates/1971/gabor-autobio.html Gachot, Bertrand www.grandprix.com/gpe/drv-gacber.html Gaddi, Taddeo www.kfki.hu/~arthp/bio/g/gaddi/taddeo/biograph.html Gadgil, Ashok web.mit.edu/invent/www/inventorsA-H/gadgil.html Gadgil, Ashok

77. MITECS: Formal Systems, Properties Of Translated in gentzen (1969). gentzen, G. (1969). The Collected Papers of Gerhardgentzen. ME Szabo, Ed. Amsterdam NorthHolland. Gödel, K. (1930). http://cognet.mit.edu/MITECS/Articles/sieg3.html

Formal Systems, Properties of Formal systems or theories must satisfy requirements that are sharper than those imposed on the structure of theories by the axiomatic-deductive method, which can be traced back to Euclid's Elements . The crucial additional requirement is the regimentation of inferential steps in proofs: not only axioms have to be given in advance, but also the logical rules representing argumentative steps. To avoid a regress in the definition of proof and to achieve intersubjectivity on a minimal basis, the rules are to be "mechanical" and must take into account only the syntactic form of statements. Thus, to exclude any ambiguity, a precise symbolic language is needed and a logical calculus. Both the concept of a "formula" (i.e., statement in the symbolic language) and that of a "rule" (i.e., inference step in the logical calculus) have to be effective; by the Church-Turing Thesis, this means they have to be recursive. See also COMPUTATION COMPUTATIONAL THEORY OF MIND LANGUAGE AND THOUGHT MENTAL MODELS ... RULES AND REPRESENTATIONS Wilfried Sieg References Frege, G. (1879).

78. Prof. Dr. Volker Peckhaus, Scientific Publications gentzen, GerhardKarl Erich (1909-45) , 23-25. Routledge Encyclopedia of Philosophy, hg. http://hrz.uni-paderborn.de/philosophie/peckhaus/peck_bib.html

79. Gödel Translate this page Quelques années auparavant, une démonstration semblable avait été apportée parGerhard gentzen (1909-1945) étudiant de Hilbert (comme Ackermann) et dont http://www.sciences-en-ligne.com/momo/chronomath/chrono2/godel.html

et portant sur les relations consistantes algorithme en introduisant les notions de fonctions (ou relations) calculables calculable et d'ensembles Dans un contexte constructiviste axiomatisables et est de Hilbert formalisme de Cantor logicisme que furent Frege et Russell et de Ackermann Hilbert (comme Ackermann et/ou l' axiome du choix elle restera non contradictoire Tarski Cohen Robinson Turing ... Church Pour en savoir plus : D.W. Baron, Ed. Dunod, Paris, 1970 Ed. Hermann, Paris, 1978-1992. Gelfond Leray

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