Bücher, kurt godel, Erstausgabe (39 Ergebnisse)

kart. Zustand: Gut. 1. Aufl. 167 S. ; 18 cm Erste Auflage, Papier lichtbedingt nachgedunkelt. ISBN 9783518281932 Sprache: Deutsch Gewicht in Gramm: 119.

Hardcover. Zustand: Very Good. No Jacket. 1st Edition.

Hardcover. Zustand: Fine. Zustand des Schutzumschlags: fine. First edition. First edition, first printing. Fine in fine dust jacket. Hardcover. 350 pp. with biliography, index. Illustrated with photographs. Biography of famed mathematician and logician Kurt Godel.

Broschiert. Zustand: Gut. 1. Aufl. 146 Seiten; Der Erhaltungszustand des hier angebotenen Werks ist trotz seiner Bibliotheksnutzung sehr sauber und kann entsprechende Merkmale aufweisen (Rückenschild, Instituts-Stempel.). Sprache: Deutsch Gewicht in Gramm: 385.

Hardcover. Zustand: Good. First Edition. Ship within 24hrs. Satisfaction 100% guaranteed. APO/FPO addresses supported.

(23 x 15,5 cm). 26 S. Mit 1 Abbildung. Original-Broschur. Zu I: Erste Ausgabe dieser für die Logik grundlegenden Arbeit. - Gödel (1906-1978), einer der bedeutendsten Logiker des 20. Jahrhunderts, setzt sich hier mit Hilberts 2. Problem auseinander, der Frage, ob sich die Arithmetik vollständig und widerspruchsfrei axiomatisieren lässt. - Klammern wie meist leicht rostig, sonst wohlerhalten. - DSB 17, 348.

Zustand: Gut. (1. Auflage). 114 Seiten; graph. Darst.; 23 cm; fadengeh. Broschur. Gutes Exemplar; minimale Gebrauchs- u. Lagerspuren. - Erstausgabe / EA. - Kurt Friedrich Gödel (* 28. April 1906 in Brünn, Österreich-Ungarn, heute Tschechien; 14. Januar 1978 in Princeton, New Jersey, Vereinigte Staaten) war ein österreichischer und später US-amerikanischer Mathematiker, Philosoph und einer der bedeutendsten Logiker des 20. Jahrhunderts. Er leistete maßgebliche Beiträge zur Prädikatenlogik (Vollständigkeit und Entscheidungsproblem in der Arithmetik und der axiomatischen Mengenlehre), zu den Beziehungen der intuitionistischen Logik sowohl zur klassischen Logik als auch zur Modallogik sowie zur Relativitätstheorie in der Physik. // Stephen Cole Kleene (* 5. Januar 1909 in Hartford, Connecticut; 25. Januar 1994 in Madison, Wisconsin) war ein US-amerikanischer Mathematiker und Logiker. Er gilt als einer der Begründer der theoretischen Informatik, besonders der formalen Sprachen und der Automatentheorie // John Barkley Rosser Sr. (* 6. Dezember 1907 in Jacksonville, Florida; 5. September 1989 in Madison, Wisconsin) war US-amerikanischer Logiker und Mathematiker. (wiki) // INHALT : Einleitung. ------ A. Intuitiver Zugang zum Gödelschen Unvollständigkeitstheorem: Die Antinomie von Richard ------ B. Die Gödelschen Theoreme. ------ 1. Das formale System ZL. ------ 2. Die Theoreme von Gödel. ------ 3. Primitiv rekursive Funktionen und Prädikate. ------ 4. Die Arithmetisierung der Metatheorie. ------ C. Die Unentscheidbarkeit der Quantifikationstheorie (Theorem von Church). ------ Vorbemerkungen. ------ 5. Allgemein-rekursive Funktionen. ------ 6. Der Gleichungskalkül von Kleene. ------ 7. Die schematische Funktionentheorie von Quine. ------ 8. Das Theorem von Church (nach Quine). ------ D. Die Verallgemeinerungen von Kleene. ------ 9. Das Kleenesche T-Prädikat. ------ 10. Das Aufzählungstheorem und seine Konsequenzen. ------ 11. Das Normalformentheorem. ------ 12. Algorithmische Theorien und das Theorem von Church in der Fassung von Kleene. ------ 13. Rekursive Auf zählbarkeit, Beweisverfahren und das verallgemeinerte Gödelsche Theorem. ------ 14. Die symmetrische Form des verallgemeinerten Gödelschen Theorems und die Unentscheidbarkeit der elementaren Zahlentheorie ------ 15. Zusammenfassung. ------ E. Anhang. ------ 16. Die Gödelsche /ß-Funktion. ------ 17. Primitiv rekursive und arithmetische Prädikate und der zahlentheoretische Formalismus. ------ Literaturverzeichnis. ------ Namen- und Sachverzeichnis. Sprache: Deutsch Gewicht in Gramm: 250.

62 Seiten plus 2 Seiten mit Porträtabbildungen, Spiralheftung, Format 14,5 x 21,2 cm, in transparenter Schutzfolie. * Enthält diverse Vorträge von H.-J. Treder aus den 90er Jahren. Zwei Vorträge thematisieren die Arbeiten bzw. Biographien von Ernst Mach und Kurt Gödel (mit Porträtabb.). Erhaltung: Auf ca. 10 Seiten Randmarkierungen mit Bleistift. Auf dem rückseitigen Umschlag ein Preis-Etikett (DM 12,00). Am Rücken hat die Spirale unten eine kleine Fehlstelle (siehe Scan). Sonst keine weiteren Mängel. Insgesamt noch gut erhalten [Eine größere Sammlung Physik, Mathematik, Astronomie und verwandte Gebiete wird derzeit in den Bestand eingearbeitet. Sie finden diese Titel bei uns in den gleichnamigen Rubriken]. Sprache: Deutsch.

Gebonden met stofomslag. Zustand: Fraai exemplaar. 1e druk. Oorspronkelijke Griekse titel: 'O Theios Petros kai Eikasia tou Goldbach' (1992). Vertaald door Peter Out. Omslag: jan de Boer. Oom Petros is het zwarte schaap van de familie. Een uitgebluste oude man die leeft als een kluizenaar, en zelfs door zijn familie wordt gezien als - een van die mislukkingen van het leven. Maar ooit was oom Petros een gevierd wiskundige. Briljant en hoogmoedig wijdde hij zijn hele leven aan een probleem dat al eeuwen elke oplossing weerstaat: het vermoeden van Goldbach. Als zijn neef dit ontdekt, begint hij een speurtocht naar oom Petros' verleden. Een levenslange obsessie lijkt uiteindelijk tot niets anders geleid te hebben dan een gebroken man. Totdat Petros door een laatste ontmoeting met zijn neef eens te meer de diepe, mysterieuze schoonheid van de wiskunde ervaart. Het Vermoeden van Goldbach is een van de oudste onopgeloste problemen in de getaltheorie en in de gehele wiskunde. Het vermoeden werd geuit in een brief die Christian Goldbach aan Leonhard Euler in 1742 schreef. Voorin dit boek staat die brief afgedrukt. Het vermoeden luidt: Elk even getal groter dan 2 kan geschreven worden als de som van twee priemgetallen (een priemgetal mag hierbij twee keer gebruikt worden). 191 pag. Size: 18cmx13,5cm.

1st ed. - (Lecture notes in logic). - Hardcover, fine.

8°, 373 S., weiße original Hefte mit schwarzer Deckel- und Rückenbeschriftung, die Rücken leicht nachgedunkelt, sonst gutes, sauberes Exemplar, teilweise noch mit original Verlagsbeilagen (hhreg) Inhalt: Heft 1: Horst Ramsenthaler: Theoretische Grundlagen der Familientherapie Ein Klärungsversuch auf der Basis de Regelbegriffs von L. Wittgenstein / Kurt Ludewig: Von Familien, Therapeuten und Beschreibungen - Vorschläge zur Einhaltung der >logischen Buchhaltungangeschlossene SystemRandolectilFamiliäre Wirklichkeiten - 10 Jahre Heidelberger FamilientherapieFeed-ForwardAutosystemische TransformationFamilien im AlltagZauberer von Oz<-Methode - ein Interview mit Steve de Shazer Buchbesprechungen: Harlod Feldmann & Margaret Feldmann: Current Controversies in Marriage and Family (K. Ley) / Douglas R. Hofstadter: Gödel, Escher; Bach. Ein Endloses Geflochtenes Band (F.B. Simon) / Frido Mann: Professor Parsifal (M. Krüll) / Dorothy M. Stetson: A Woman's issue (K. Ley) / Jürg Willi: Koevolution (E. Sperling) / Robert L. Ziffer: Adjunctive Techniques in Family Therapy (T. Hubschmid).

Leipzig & Berlin, B.G. Teubner, 1932. 8vo. A mint copy, in the original wrappers, still contained in the original plastic protection. In "Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Manger, Heft 2". Pp. 27-28. [Entire volume: 38 pp]. First edition of Gödel's important paper, which constitutes a supplement to his "Die Vollständigkeit der Axiome des logischen Funktionskalküls" (1930). In the present paper, Gödel seminally formulates his earlier incompleteness results from the standpoint of first-order logic, thereby contributing substantially to modern mathematical logic."In 1932 Godel published his formulation of the incompleteness results from the standpoint of first order logic. If number theory is regarded as a formal system in first-order logic, then the above results about incompleteness and unprovability of consistency apply to S. If, however, S is extended by variables for sets of numbers, for sets of sets of numbers, and so on (together with the corresponding comprehension axioms), then we obtain a sequence of systems S" the consistency of each system is provable in all subsequent systems. But in each subsequent system there are undecidable propositions. Going up in type in this way, he noted, corresponds in a type-free system of set theory to adding axioms that postulate the existence of larger and larger infinite cardinalities. This was the beginning of Gödel's interest in large cardinal axioms, an interest that he elaborated in 1947 in regard to the continuum problem." (DSB).The issue contains several papers by Karl Menger.

First edition in English, first impression, of the famed incompleteness theorems, overturning a century of efforts to place the whole of mathematics on an axiomatic basis and proving that the bounds cannot be those of one formal system. This edition includes a preface by R. B. Braithwaite (1900-1990), Knightbridge Professor of Moral Philosophy at Cambridge. For Gödel, even in elementary arithmetic there exist propositions that cannot be proven or disproven within the system. Mathematics is not finished, as had been believed, and computers can never be programmed to answer all mathematical questions. The theorems were originally published in Monatshefte für Mathematik in 1931. Newman, pp. 1668-95. Octavo. Formulae in the text. Original light green cloth, spine lettered in red. With dust jacket. With bookseller's ticket of Dillon's University Bookshop, London, to front pastedown. Boards gently splayed, rear cover faintly mottled; jacket unclipped, spine toned, extremities creased, closed tears to rear cover sometime repaired with tape on recto and verso: a very good copy in like jacket.

Zustand: Very Good. First Edition. Kurt Gödel's "Zum Entscheidungsproblem des logischen Funktionenkalküls," published in Monatsheften für Mathematik und Physik, vol. 40. Complete volume, Pp. 470, 41 "Literaturberichte," with Gödel's paper on pp. 433-443. Bound without wraps in modern grey suede-like binding with spine lettered in gilt. Pages toned, lightly bumped at corners. Gödel's work here on the decision problem in formal mathematical systems would be central to Alan Turing and Alonzo Church's work, leading to the Church-Turing thesis. "Gödel's achievement in modern logic is singular and monumental -- indeed it is more than a monument, it is a landmark which will remain visible far in space and time. The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement" (John von Neumann, quoted in Halmos, The American Mathematical Monthly. Gödel is considered alongside Aristotle to be one of the most important logicians in history.

Zustand: Very Good. First Edition. Kurt Gödel's paper "Die Vollständigkeit der Axiome des logischen Funktionenkalküls," published in Monatsheften für Mathematik und Physik, vol. 37. Complete volume, Pp. [iv], 404, 52 "Literaturberichte," with Gödel's paper on pp. [349]-360. Bound without wraps in modern grey suede-like binding with spine lettered in gilt. Pages toned and contents marked several times throughout with an ink stamp of a seashell, none appearing on Gödel's paper. Gödel's first proof of his completeness theorem, a re-written and more concise version of Gödel's doctoral 1929 dissertation with more succinct explanations and omitting the lengthy introduction. It is the first major publication by one of the most important figures in 20th-century mathematics. "Gödel's achievement in modern logic is singular and monumental -- indeed it is more than a monument, it is a landmark which will remain visible far in space and time. The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement" (John von Neumann, quoted in Halmos, The American Mathematical Monthly. Gödel is considered alongside Aristotle to be one of the most important logicians in history.

Washington, 1938 & 1939. Royal8vo. 2 volumes, uniformly bound in contemporary full cloth with gilt lettering to spine. Exlibris to front paste down. In "Proceedings of the National Academy of Science", vol. 24 and 25. Fine and clean. Pp.556-57" Pp. 220-24). [Entire volumes: VII, 572 pp. VII, 661 pp]. First edition of arguable Gödel's most important publications only second to his incompleteness theorem. The first problem of Hilbert's famous 1900 address asks for a proof of Cantor's continuum hypothesis. Hilbert considered this problem one of the most important problems confronting the mathematical world. As a first step towards such a proof Ernst Zermelo proved in 1904 another hypothesis by Cantor, namely that every set can be well ordered. In his proof Zermelo introduced a necessary tool which later became known as the axiom of choice. Because of its non-constructive nature this axiom, and the continuum hypothesis, became the object of much controversy in the mathematical community. Gödel's results on this topic are, besides his completeness and incompleteness theorems, his most celebrated. During the autumn terms of 1938 and 1939 Gödel delivered a series of lectures at the Institute for Advanced Study, in which he proved that the axiom of choice and the generalized continuum hypothesis are consistent with the other axioms of set theory if these axioms are consistent.

Leipzig & Berlin, B.G. Teubner, 1932. 8vo. In the original wrappers. In "Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Menger, Heft 3". A near mint copy, Pp. 12-13" Pp. 20-21. [Entire volume: 26 pp]. First printing of these two important papers both closely related to Gödel landmark paper Über formal unentscheidbare Sätze". Here Gödel applies the extensions of the incompleteness theorems to a wider class of formal systems : "is already the more modern first-order Peano arithmetic, the system in which Godel in his abstract described his incompleteness results. The passage [in the present paper] envisages the introduction of higher-type variables, which would have the effect of re-establishing the system P, but as one proceeds to higher and higher types, that "all the [unprovable] propositions constructed are expressible in Z (hence are number-theoretic propositions)" is an important point about incompleteness. The last sentence of the [1932] passage is Godel's first remark on set theory of substance, and significantly, his example of an "axiom of cardinality" to take the place of type extensions is essentially the one that both Abraham Fraenkel [1922] and Thoralf Skolem [1923] had pointed out as unprovable in Ernst Zermelo's [1908] axiomatization of set theory and used by them to motivate the axiom of Replacement. " (Kanamori, Gödel and Set Theory). "By invitation, in October 1929 Gödel began at tending Menger's mathematics colloquium, which was modeled on the Vienna Circle. There in May 1930 he presented his dissertation results, which he had discussed with Alfred Tarski three months ear lier, during the latter's visit to Vienna. From 1932 to 1936 he published numerous short articles in the proceedings of that colloquium (including his only collaborative work) and was coeditor of seven of its volumes. Gödel attended the colloquium quite regularly and participated actively in many discus sions, confining his comments to brief remarks that were always stated with the greatest precision." (DSB).

[Leipzig, 1930). 8vo. Stapled extract. Some flossing to inner margin, probably from when extracted, far from affecting text. Handwritten indication of the journal, from which it is extracted, in pencil, on top of first page. Pp. (349) - 360. The scarce first printing of this seminal paper, in which Gödel, the greatest logician since Aristotle, proves for the first time the compactness theorem, which is of the greatest importance to the development of model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent. The compactness theorem is used by Gödel to derive a generalization of the completeness theorem. The present highly important and influential paper constitutes a revised and shortened version of Gödel's doctorial dissertation, published the same year, in which he showed that every valid formula of first-order logic is provable and, moreover that each axiom of first-order logic is independent (the first of which is referred to as Gödel's completeness theorem). In this journal version he, in addition to that proved in the dissertation, also proved his highly influential compactness theorem (which states that a set of first-order sentences has a model if and only if every finite subset of it has a model). "G settled the [problem] of completeness (positively) in the summer and wrote up the result as his dissertation, which was finished by July. A revised version was received by the editor of "Monatshefte" on 22 October and published 1930" a main addition was what is now known as "Compactness theorem". G received his doctoral degree on 6 February 1930. He presented his result in Menger's colloquium on 14 May and in Königsberg on 6 September 1930." (Wang, Reflections on Kurt Gödel). "The Compactness Theorem was extended to the case of uncountable vocabularies by Maltsev in 1936, from which the Upward Löwenheim-Skolem theorem immediately follows. The Compactness Theorem would become one of the main tools in the then fledgling subject of model theory." (SEP).From the library of the highly important Danish logician and philosopher Jørgen Jørgensen (1894-1969), who was an active collaborator with the logical positivists from the Vienna Circle. After Hans Hahn's death he became editor of the series of the Vienna Circle, the "Einheitswissenchaft" ("Unified Science"), and later he collaborated on the International Encyclopedia, to which he contributed with the essay "The Development of Logical Empiricism", 1951. Jørgensen is also widely recognized for his three volume work "Treatise of Formal Logic" Its Evolution and Main Branches, with its Relations to Mathematics and Philosophy", 1931.Apart from the paramount importance of the paper, it is also of the utmost rarity, as evidenced by the fact that it is neither present in the collection of Honeyman, Barchas, Haskell Norman, nor Hook & Norman: Origins of Cyberspace, and furthermore, the paper has not been up for sale on any of the major auction houses for at least the last 50 years.

Neuchâtel, Dialectica, 1958. 8vo. Original printed wrappers. The entire issue 47/48 offered here. Uncut and unopened. First edition of Gödel's 'Dialectica-paper' in which he presented his consistency proof for arithmetic. In 1931 Gödel formulated and proved his second incompleetness theorem" that the consistency of Peano arithmetic cannot be proved using Peano arithmetic itself or any of its direct extensions. The title of Gödel's famous 1931 paper (Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I) states that it is the first part of several papers. Gödel mentions, in a footnote, that the second part of his paper will deal with the source of the incompleteness of formal systems using the theory of types. But no actual continuation of Gödel's 1931 paper ever appeared. However, in his 1958 "Dialectica-paper" (the offered item) Gödel showed how type theory can be used to give a consistency proof for arithmetic. In this paper Gödel furthermore discussed some of the philosophical implications of his results. Paul Bernays thought highly of this paper, and planned to publish an English translation, but during the revision of the paper Gödel became dissatisfied with the philosophical introduction and rewrote it completely. When the proof sheets of the revised paper arrived from the printer, Gödel once again became unpleased with the sections concerning his philosophical views. He never returned the proof sheets. The issue offered, which is a festschrift on the occasion of Paul Bernay's 70th birthday, furthermore contains original contributions by Ackermann, Carnap, Curry, Fraenkel, Robinson, Skolem.

First Paperback Edition. 8vo. softback. [xvii] + 532pp, indexed, with b/w illustrations. A clean copy with no previous owners' markings or inscriptions. Front top outer corner a little bumped, rear cover top corner creased. VG overall. (Shelf 202 BOX 10) ISBN: 0195147227 PLEASE NOTE: Heavy BOOK (1kg +) Postage rates vary according to destination, weight and speed. For an accurate overseas quote PLEASE either call or email us before ordering. (AbeBooks shipping quote is based on items weighing up to 1 kilo only).** Pictures available upon request, if not already displayed here.** Visit our homepage for our shop opening hours. Over 20,000 books in stock - come and browse. PayPal, credit and most debit cards welcome. Books posted worldwide. For any queries please contact us direct.

souple. Zustand: Assez bon. 1 brochure in-8, Association des professeurs de mathématiques de l'enseignement public (A. P. M.) Cahors, impr. A. Coueslant (1962), 38 pp. Etat très satisfaisant (couv. empoussierrée) pour cette petite rareté par Jean Balibar (1915-2008). agrégé de Mathématiques (1938), qui commença par enseigner au lycée Condorcet avant la guerre, et qui devint professeur à l'Université de Tours. Langue: Français.

23,5 x 15,5 cm. Zustand: Gut. 1. Edition. X, 182 Seiten ; Mit Figuren Innen sauberer, guter Zustand. Leineneinband, mit den üblichen Bibliotheks-Markierungen, Stempeln und Einträgen, innen wie außen, siehe Bilder. (Evtl. auch Kleber- und/oder Etikettenreste, sowie -abdrücke durch abgelöste Bibliotheksschilder). Einband wenig berieben. In Englisch B13-04-03A|S37 Sprache: Englisch Gewicht in Gramm: 440.

24 x 17 cm. Zustand: Gut. 1. Auflage. 225 Seiten ; Mit zahlreichen Abbildungen Text in deutsch und englisch. - Original Pappband mit Bibliotheksrückenschild im sehr guten Zustand. Innen mit Bibliotheksstempeln, sehr sauberes Exemplar B15-01-01A|S67 Altersfreigabe FSK ab 0 Jahre Sprache: Deutsch Gewicht in Gramm: 508.

Gr.8°, 137 S., Broschur, Tadell. m- Kurt Gödel's famous First Incompleteness Theorem shows that, for any sufficiently rich theory that contains enough arithmetic, there are some arithmetical truths the theory can express but cannot prove. How is this remarkable result established This short book explains. It also discusses Gödel's Second Incompleteness Theorem. The aim is to make the Theorems available, clearly and accessibly, even to those with a quite limited formal background. The first edition was based on much-downloaded lecture notes for a course given in Cambridge for many years. This second edition is expanded and extensively revised. Dieses Buch befindet sich in unserem Aussenlager; sollten Sie dieses im Laden abholen wollen, bitten wir Sie um vorgängige Nachricht. 1100 gr. Schlagworte: Mathematik , Philosophie, Naturwissenschaft.

Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Near Fine. First edition. 8vo. [4], v-x, 1-182 pp. Black cloth with silver lettering on the spine. Jacket design by Dennis M. Arnold. Yourgrau's volume explores the published and unpublished writings of Gödel, specifically his works on time and questions regarding its metaphysical status. The nature and meaning of time and its implications on existence in general are explored here in-depth. Light foxing to the textblock.

Softcover. Zustand: Near Fine. First edition (Stated "Preliminary Edition"). Quarto. 117pp. Line drawings, diagrams, and formulas. Printed beige wrappers. Former owner's signature on front wrap, else about fine. Preliminary edition of a book subsequently published by Holt Rinehart Winston in 1945 that became an important textbook. Wolfe claimed the 1945 edition was the first "fairly complete, elementary book published on Non-Euclidean geometry in America." The impact of non-Euclidean geometry on the development of mathematics cannot be over estimated. The discovery lead to an entire reevaluation of the foundations of mathematics and of the axiomatic method in particular. The certainty of the Greeks, ultimately gave way to the theorems of Kurt Gödel in the 1930s and the property of incompleteness. The book gives the history of the development and the foundations of standard geometry and their evolution. From the introduction: "This book has been written in an attempt to provide a satisfactory textbook to be used as a basis for elementary courses in Non-Euclidian Geometry. The need for such a volume, definitely intended for classroom use and containing substantial lists of exercises, has been evident for some time. It is hoped that this one will meet the requirements of those instructors who have been teaching the subject regularly, and also that its appearance will encourage others to institute such courses. The benefits and amenities of a formal study of Non-Euclidean Geometry are generally recognized. Not only is the subject matter itself valuable and intensely fascinating, well worth the time of any student of mathematics, but there is probably no elementary course which exhibits so clearly the nature and significance of geometry and, indeed, of mathematics in general. However, a mere cursory acquaintance with the subject will not do. One must follow its development at least a little way to see how things come out, and try his hand at demonstrating propositions under circumstances such that intuition no longer serves as a guide. For teachers and prospective teachers of geometry in the secondary schools the study of Non-Euclidean Geometry is invaluable." Rare.

Berlin, Springer, 1928. Orig. full cloth. Lower part of spine with loss of cloth. Lower right cornerof titlepage cut away, no loss of letters. VIII,120 pp. First edition. (Die Grundlehren der Mathematischen Wissenshaften in Einzeldarstellungen, Band XXVII). In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever.

Berlin, Julius Springer, 1928. 8vo. Publisher's full cloth. Ink signature of Samuel Skulsky on front free end paper. Completely clean throughout. A fine and tight copy. First edition of the foundation of modern mathematical logic.In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever. Scarce in this condition.

Berlin, Springer, 1928. 8vo. Uncut in orig. printed wrappers. VIII,120. With the name of Bent Schultzer (Former Danish professor in philosophy) on first leaf. Internally clean. First edition. (Die Grundlehren der Mathematischen Wissenshaften in Einzeldarstellungen, Band XXVII). In the years 1917-22 Hilbert gave three seminal courses at the Univeristy og Göttingen on logic and the foundation of mathematics. He received considerable help in preperation and eventual write up of these lectures from Bernays. This material was subsequently reworked by Ackermann into the monograph 'Grundzüge der Theoretischen Logik' (the offered item). It containes the first exposition ever of first-order logic and poses the problem of its completeness and the decision problem ('Entscheidungsproblem'). The first of these questions was answered just a year later by Kurt Gödel in his doctorial dissertation 'Die Vollständigkeit der Axiome des logischen Funktionenkalküls'. This result is known as Gödel's completeness theorem. Two years later Gödel published his famous 1931 paper 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I' in which he showed that a stronger logic, capable of modeling arithmetic, is either incomplete or inconsistent (Gödel's second incompleteness theorem). The later question posed by Hilbert and Ackermann regarding the decision problem was answered in 1936 independantly by Alonzo Church and Allan Turing. Church used his model the lambda-calculus and Turing his machine model to construct undecidable problems and show that the decision problem is unsolvable in first-order logic. These results by Gödel, Church, and Turing rank amongst the most important contributions to mathematical logic ever.

Original offprint of a paper read by Ramsey to the London Mathematical Society on December 13 1928, "primarily concerned with a special case of one of the problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula" p. 264.) This problem is commonly known as the Entscheidungsproblem, or "decision problem", and had been a source of keen debate among logicians before it was proven by Kurt Gödel in 1931 and Alonzo Church in 1936 that David Hilbert, and the other members of the formalist school of anti-logistic mathematics, were mistaken: all arithmetic systems must contain propositions which are not provable in that system. "Ramsey's main interest in mathematics was in its foundations. His 'The foundations of mathematics', read to the London Mathematical Society on 12 November 1925, was the culmination of the reduction of mathematics to logic undertaken in Russell's and Whitehead's Principia mathematica (1913). On mathematics itself he published only eight pages, 'On a problem of formal logic' (read to the London Mathematical Society on 13 December 1928), but this has since become the basis of a branch of mathematics known as Ramsey theory" (OBNB.) Risse III, 132. Octavo, pages [263]-286 + final blank leaf. Wire-stitched as issued in printed grey paper wrappers. Staples slightly corroded, else a very good copy.