consistency continuum hypothesis von godel kurt (23 Ergebnisse)

Paperback. Zustand: As New. No Jacket. Pages are clean and are not marred by notes or folds of any kind. ~ ThriftBooks: Read More, Spend Less 0.35.

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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 03 GOE 9780691079271 Sprache: Englisch Gewicht in Gramm: 550.

Hardcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 03 GOE 9780691079271 Sprache: Englisch Gewicht in Gramm: 550.

Zustand: Fine. 13th printing (1999), 72 pp., Paperback, fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

Paperback. Zustand: Brand New. 86 pages. 9.00x6.00x0.21 inches. In Stock.

Zustand: Good. Princeton University Press, 1951. Originally published in 1940, this is the second printing with "new" notes; cover lightly soiled/rubbed/bumped, previous owner's name inscribed on cover in black ink, corners lightly rubbed, spine ends quite rubbed; edges lightly soiled; ffep has faint erasures and previous owner's name/date in black ink; binding tight; cover, edges, and interior intact and clean except as noted. paperback. Good.

Zustand: New.

Paperback. Zustand: New. Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Godel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Gottingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Godel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk.He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

Zustand: New. 1940. Paperback. . . . . . Books ship from the US and Ireland.

paperback. Zustand: Good. softcover book light wear to cover and book edges, has some light reader wear.

Paperback. Zustand: Brand New. 69 pages. 9.50x6.00x0.25 inches. In Stock.

Paperback. Zustand: New. Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Godel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Gottingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Godel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk.He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

Soft cover. Zustand: Near Fine. No Jacket. First Edition, Fourth Printing. ***** This is the first edition, fourth printing (with "Fourth Printing, 1958" stated on the copyright page). ***** This book is SIGNED by the author (Kurt Godel) on the first page. The author did not inscribe this book to anyone; it is just signed by him. ***** Very nice softcover without dust jacket (as issued). There is NO writing, NO bookplates, and NO remainder marks. It is NOT a book club edition and NOT a former library book. ***** CONDITION: This book is in NEAR FINE condition. ***** OUR GUARANTEE TO YOU: All books are guaranteed to be as described. We believe that no sale is complete until you are happy. Any book is returnable for a full refund (including postage) if you're not 100% satisfied. All books are packaged very carefully and shipped via insured USPS Mail with Delivery Confirmation. ***** Thank you! Richard Vick, Modern First Editions (Buying and Selling Modern First Editions since 1982). Signed by Author(s).

Zustand: Near Fine. Princeton 1970 (1940) Seventh Edition. 1940 Annals of Mathematics Studies No 3. 8vo., 72pp., wraps. Near Fine.

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

Soft cover. Zustand: Very Good. 1st Edition. First edition, first printing, of Gödel's seminal work, the full title being 'The Consistency of the Axiom of Choice and of the Generalised Continuum-Hypothesis with the Axioms of Set Theory', arguably the major achievement of his life as a mathematician and set theorist. This edition presents a revised collection of the lectures first delivered at Princeton in 1938, accompanied by notes from the statistician and game theorist George W. Brown. Published by Princeton University Press in 1940, and overall a very good copy, with some fading to the extremities and a small tear to the lower corner of the rear wrappers. This copy comes from the library of Morton White, Gödel's colleague at the Institute for Advanced Study, and includes his ownership signature to the front pastedown.

Hardcover. Zustand: Near Fine. Gödel, Kurt. "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis", in Proceedings of the National Academy of Sciences, vol 24, pp.556-557, 1938, in the volume of 572pp.__+__ Offered with: _____. "Consistency-proof for the Generalized Continuum-Hypothesis", in Proceedings of the National Academy of Sciences, vol 25 pp. 220-224, 1939, in the volume of 661pp. Both first editions, and uniformly bound in brown cloth, nicely imprinted in gilt (with the full name of the journal, which is unusual given its length). There are some rubbed places on the covers and along spine bottom, making those areas a light shade of brown. Small 6x8mm perforated stamp on title; the text is in very fine condition. Overall, a solid near-Fine on both volumes.__+__ These works are arguably Gödel 's next most important contributions next to the incompleteness theorems, which are arguably mathematical logic's most important achievement in the 20th century. Hilbert famously put forward a list of 23 important questions in mathematics, 10 of which were presented at the International Congress of Mathematics in Paris in 1900. The very first of these questions was the continuum hypothesis, a problem simply stated: .how many points on a line are there? Strangely enough, this simple question turns out to be deeply intertwined with most of the interesting open problems in set theory, a field of mathematics with a very general focus, so general that all other mathematics can be seen as part of it, a kind of foundation on which the house of mathematics rests. Most objects in mathematics are infinite, and set theory is indeed just a theory of the infinite. --Juliette Kennedy, Can the Continuum Hypothesis Be Solved? , 2011, on the IAS website.__+__ "In 1935 Godel had made the first breakthrough in his new area of research: set theory. During May and June 1937 he lectured at Vienna on his striking result that the axiom of choice is relatively consistent. That summer he obtained the much stronger result that the generalized continuum hypothesis is relatively consistent; and in September 1937 John von Neumann, an editor of the Princeton journal Annals of Mathematics, urged him to publish his new discoveries there. Yet Gödel did not announce them until November 1938, and then not in the Annals but in a brief summary communicated to the Proceedings of the National Academy of Sciences. --Complete Dictionary of Scientific Biography.__+__ On the continuum Hypothesis: Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain (Dauben 1990). It became the first on David Hilbert's list of important open questions that was presented at the International Congress of Mathematicians in the year 1900 in Paris. Axiomatic set theory was at that point not yet formulated. Kurt Gödel proved in 1940 that the negation of the continuum hypothesis, i.e., the existence of a set with intermediate cardinality, could not be proved in standard set theory. The second half of the independence of the continuum hypothesis i.e., unprovability of the nonexistence of an intermediate-sized set was proved in 1963 by Paul Cohen. --Wikipedia __+__ On Gödel , in general: "The character and achievement of Gödel, the most important logician since Aristotle, bear comparison with those of the most eminent mathematicians. His aversion to controversy is reminiscent of Newton s, while his relatively small number of publications each quite precise and almost all making a major contribution echo Gauss s motto of few but ripe. Like Newton, he revolutionized a branch of mathematics in this case, mathematical logic giving it a structure and a Kuhnian paradigm for research. His notebooks, like those of Gauss, show him to be well in advance of his contemporaries. While Newton made substantial efforts in theology as well as in mathematical physics." --Complete Dictionary of Scientific Biography.

Soft cover. Zustand: Very Good. 1st Edition. First edition, complete journal issue in original printed wrappers, of Gödel's milestone paper proving the consistency of the Axion of Choice and the Generalized Continuum Hypothesis with the axions of set theory. In 1878, German mathematician Georg Cantor put forward the 'continuum hypothesis': any infinite subset of the set of all real numbers can be put into one-to-one correspondence either with the set of integers or with the set of real numbers ("There is no set whose cardinality is strictly between that of the integers and that of the real numbers"). This was the first in Hilbert's famous list of mathematical problems, presented in an address to the International Congress of Mathematicians at Paris in 1900. All attempts to prove or disprove the hypothesis failed until 1938, when Kurt Gödel, in this paper, showed that it was impossible to disprove the continuum hypothesis. "Gödel studied the relationship of the continuum hypothesis and the axiom of choice to basic set theory as formulated by the mathematicians Ernst Zermelo and Abraham Fraenkel . . . Gödel showed that both the continuum hypothesis and the axiom of choice are consistent with the axioms of set theory. More precisely, he demonstrated that if the Zermelo-Fraenkel system without the axiom of choice is consistent, then the Zermelo-Fraenkel system with the axiom of choice is consistent, and that the continuum hypothesis is consistent with the Zermelo-Fraenkel system" (Ryan, Thinkers of the Twentieth Century, p. 212f). "Godel's result, joined to Cohen's (1963-1964), set the stage for a whole new era in the theory of sets in which a host of problems of the consistency or independence of various conjectures in set theory relative to this or that set of axioms are being investigated by constructing models" (Shanker, Godel's Theorem in Focus, 66-67). According to the Stanford Encyclopedia of Philosophy, "the principle of set theory known as the 'Axiom of Choice' has been hailed as 'probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid's axiom of parallels which was introduced more than two thousand years ago" (Stanford Portal; Fraenkel, 1973, II.4). Note that Godel's booklet 'The Consistency of the Continuum Hypothesis' (Princeton, 1940) is a collection of notes from Gödel's lectures published two years after this original document. 8vo, pp. 525-572, vii (volume title and index) (small area of damage to upper outer corner of volume title due to adhesion to following leaf of index, tiny spot of dampstaining affecting upper margin of pp. 525-526 & 553-564, nowhere near text). Original printed wrappers (lightly creased, ends of spine a little worn).

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.

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Taschenbuch. Zustand: Neu. Consistency of the Continuum Hypothesis | Kurt Gödel | Taschenbuch | Einband - flex.(Paperback) | Englisch | Princeton University Press | EAN 9780691079271 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty.His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem.In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.