11 books for « godel kurt »Edit

‎Über Vollständigkeit und Widerspruchsfreiheit (+) Eine Eigenschaft der Realisierungen des Aussagenkalküls.‎

‎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)‎

‎Die Vollständigkeit der Axiome des logischen Funktionskalküls. [In: Monatshefte für Mathematik und Physik, XXXVII. Band]. - [THE COMPACTNESS THEOREM]‎

‎[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.‎

‎Ein Spezialfall des Entscheidungsproblems der theoretischen Logik. - [INCOMPLETENESS FROM THE STANDPOINT OF FIRST-ORDER LOGIC]‎

‎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.‎

‎Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. (In: Dialectica, volume 12, pp.280-87). - [GÖDEL'S FINAL PAPER]‎

‎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.‎

‎The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis (+) Consistency-proof for the Generalized Continuum-Hypothesis. - [THE CONSISTENCY OF SET THEORY]‎

‎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. ‎

‎Ergebnisse eines mathematischen Kolloquiums, unter Mitwirkung von Kurt Gödel und Georg Nöbeling, herausgegeben von Karl Menger, Heft 1.‎

‎Leipzig & Berlin, Teubner, 1931. 8vo. In the original printed wrappers still contained in the original plastic protection. A little rust coming of the staples as usual. A near mint copy. 31 pp.‎

‎The rare first appearance of the first publication (Heft 1) of the proceedings of the famous mathematics colloquium founded by Karl Menger, which came to include some of the 20th century most influential and important mathematicians.‎

‎La prova matematica dell'esistenza di Dio (Incipit)‎

‎Bollati Boringhieri 2006 123 pages 11x1 8x17 6cm. 2006. Broché. 123 pages.‎

‎Très bon état‎

‎The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. (Annals of Mathematics Studies Number 3). Third printing.‎

‎Princeton, Princeton University Press, 1953. 8vo. Original stiff wrappers. (8),69,(3) pp.‎

‎LE THEOREME DE GODEL‎

‎SEUIL. 1989. In-8. Broché. Bon état, Couv. convenable, Dos satisfaisant, Intérieur frais. 178 pages.. . . . Classification Dewey : 800-LITTERATURE (BELLES-LETTRES)‎

‎ Classification Dewey : 800-LITTERATURE (BELLES-LETTRES)‎

‎LE THEOREME DE GODEL‎

‎COLLECTION SOURCES DU SAVOIR-TRADUCTIONS DE L'ANGLAIS ET DE L'ALLEMAND PAR JEAN-BAPTISTE SCHERRER-190 PAGES-14 CM X 20,5 CM-(17E)‎

‎SEUIL COUVERTURE SOUPLE ETAT NEUF‎

‎A logical Journey. From Gödel to Philosophy.‎

‎ Cambridge (MA) MIT Press, 1996, format in-8°, 355 pp, Volume 295 of the ''Synthese Library''. Fine copy of the original hardback edition with a fine original dust jacket. No library markings.‎