set theory continuum (27 Ergebnisse)

Zustand: Good. Former library copy. Pages intact with minimal writing/highlighting. The binding may be loose and creased. Dust jackets/supplements are not included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good.

Paperback. Zustand: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less.

Zustand: Very Good. 154 pp., Paperback, previous owner's name to the title page, else very good. - 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.

Zustand: Very Good. 4th printing (1958), 72 pp., Paperback, very good. - 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. 160 pages. 9.00x6.00x0.50 inches. In Stock.

Zustand: Poor. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. Clean from markings. In poor condition, suitable as a reading copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,350grams, ISBN:

Zustand: Fair. Acceptable condition. No Dust Jacket (mathematics, math, set theory) A readable, intact copy that may have noticeable tears and wear to the spine. All pages of text are present, but they may include extensive notes and highlighting or be heavily stained. Includes reading copy only books.

Paperback. Zustand: Brand New. revised edition. 315 pages. 9.25x6.25x1.00 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.

Softcover. Zustand: Sehr gut. N.Y., Dover (2008). XXV, 154 p. Pbck. Name verso frontcover and on title.

Kartoniert / Broschiert. Zustand: New.

Hardcover. Zustand: Gut. New York, Benjamin 1966. 154 p. Ocloth. with dust jacket. (dust jacket slightly browned and with small tear).

Taschenbuch. Zustand: Neu. Neuware - This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.

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

23 x 15 cm, paperback, viii, 70 pages, Text in English, covers plasticised, edges of some pages slightly damaged, paper aged toned, although still in good condition, see picture. Annals of Mathematics Studies. Number 3. 144g.

Zustand: New. In.

Hardcover. Zustand: FINE. First Edition. 302pp. 8vo, sewn binding in navy cloth. FINE copy, entirely clean and sharp, sans jacket as issued uniformly with the series.

Zustand: New.

Paperback. Zustand: Brand New. reprint edition. 425 pages. 9.25x6.10x1.00 inches. In Stock.

Taschenbuch. Zustand: Neu. Set Theory of the Continuum | Haim Judah (u. a.) | Taschenbuch | ix | Englisch | 2012 | Springer | EAN 9781461397564 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Primarily consisting of talks presented at a workshop at the MSRI during its 'Logic Year' 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include : J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

4to. 154 pp. Encuadernación editorial. Excelente estado.

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

Hardcover. Zustand: Near Fine. First edition. 8vo. [4], v-ix, [1], 1-416, [5] pp. Glossy paper boards printed in blue and black, no dust jacket (Springer-Verlag mathematics titles of this period were typically issued without jackets). Volume 26 in the Mathematical Sciences Research Institute Publications series. A collection of papers presented at the eponymous workshop organized by Hugh Woodin in 1989. Includes papers by the editors, Mac Lane, Soare, Shelah, and many others. A Near Fine book with toning to the boards.

Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Very Good. First trade edition. 8vo. [6], 1-154 pp. Grey cloth with white lettering on the spine. The first trade publication of Cohen's hugely influential work. A detailed exposition of Cohen's work on proving the independence of the continuum hypothesis (and the Axiom of Choice) from Zermelo-Frankel set theory. Cohen's method of forcing, used to establish these results, proved to be a powerful and fruitful technique in contemporary set theory. Cohen was awarded a Fields Medal for his work. The volume consists of Cohen's lecture notes supplemented by background material in logic and axiomatic set theory, and an account of Godel's proof of the consistency of the continuum hypothesis. Light bumping to the corners; jacket with a closed tear and rubbing on its front panel, rubbing on the jacket's rear panel.

First edition. The Method of Forcing and the Continuum. First edition, extremely rare offprints, of Cohen?s proof that the continuum hypothesis (CH) and the axiom of choice (AC) cannot be proved from the generally accepted Zermelo-Fraenkel axioms (ZF) of set theory; the method of ?forcing? which Cohen devised for the purposes of his proof revolutionized the subsequent development of set theory. Kurt G?del wrote in 1964 that this work ?no doubt is the greatest advance in the foundations of set theory since its axiomatization? (G?del, Works 2, p. 270). G?del had proved in 1938 that CH and AC cannot be disproved from ZF ? Cohen?s and G?del?s results together showed that CH and AC are independent of ZF. G?del had, in fact, also proved that AC could not be proved from ZF, although he never published this result, but his methods had failed to establish this for CH. 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. The ?Axiom of Choice?, proposed by the German logician Ernst Zermelo in 1904, states that, given any collection of sets (even an infinite collection), each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set. ?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 Encyclopedia of Philosophy). All attempts to prove or disprove CH or AC failed until the work of G?del and Cohen. For this work, Cohen was in 1966 awarded a Fields Medal (the equivalent for mathematics of a Nobel Prize). Just as G?del followed up his 1938 announcement with a monograph based on a series of lectures, published in 1940 by the Princeton University Press, so Cohen followed up his announcement with a monograph entitled Set Theory and the Continuum Hypothesis, which acted as a very readable introduction to both set theory and his remarkable results. Cohen?s offprints and book are accompanied here by an autograph letter from Cohen to the mathematician Martin Davis, whom Cohen writes was ?directly responsible for my looking once more at set theory? RBH lists one other copy of each offprint. Not on OCLC. Provenance:?Martin?Davis (1928-2023), American logician and computer scientist (ownership signature and his notes on Set Theory and the Continuum Hypothesis; ALS from Cohen to Davis). Two problems had preoccupied workers in the field of set theory since its creation by Cantor beginning in the 1870s: the well-ordering principle and the cardinality of the continuum. An ?ordering? of a set X is a rule for deciding, given any two different elements of X, which one precedes the other (such as the usual ordering on the set of integers ?, ?2, ?1, 0, 1, 2, ?). A ?well-ordering? of X is an ordering with the property that every non-empty subset Y of X has a least element (an element that precedes all the other elements of Y). So the usual ordering of the integers is not a well-ordering (there is no least integer), but the same ordering on the set of positive integers is a well-ordering. ?Cantor had conjectured the proposition, now called the ?well-ordering theorem,? that every set can be well-ordered. In 1904 Zermelo gave a proof of this conjecture, using in an essential way the following mathematical principle: for every set X there is a ?choice function,? f, which is defined on the collection of non-empty subsets of X, such that for every subset A of X,f(A) is an element of A [so f ?chooses? an element of each subset of X]. Subsequently, in 1908, Zermelo presented an axiomatic version of set theory in which his proof of the well-ordering theorem could be carried out. One of the axioms was the principle just stated, which Zermelo referred to as the ?Axiom der Auswahl? (the Axiom of Choice, abbreviated AC). ?Zermelo?s proof was the subject of considerable controversy. The well-ordering theorem is quite remarkable, since, for example, there is no obvious way to define a well-ordering of the set of real numbers. Nor is such an explicit well-ordering provided by Zermelo?s proof. Thus, many people who thought Zermelo?s result implausible cast doubt upon the validity of AC. The other set-existence axioms all have the form that some collection of sets, explicitly definable from certain given parameters, is itself a set. The axiom of choice, on the other hand, asserts the existence of a choice function but does not provide an explicit definition of such a choice function. Zerrnelo was well aware that his axiom had this purely existential character, but many other mathematicians were uncomfortable with existence proofs that did not provide the construction of specific examples of what was asserted to exist? (G?del, Works 2, pp. 1-2). Beginning in 1874, Cantor introduced the concept of the ?cardinality? of a set. For a set with a finite number of elements, its cardinality is just the number of elements in the set. But the cardinality is also defined for infinite sets. Two sets have the same cardinality if and only if they can be put into one-to-one correspondence. If ? is the cardinal number of a set X, the cardinal number of the set of all subsets of X is denoted by 2?(because if a finite set has n elements, the set of all its subsets has 2n elements). A set X has cardinality less than or equal to that of another set Y if X can be put into one-to-one-correspondence with a subset of Y. The smalle.

Washington, 1963-64. 8vo. The two complete volumes 50 and 51 of the 'Proceedings of the National Academy of Sciences' in contemporary half cloth bindings + original printed wrappers. First editions. In this work Cohen established the independence of the Axiom of Choice (AC) from ZF and the independence of the Continuum Hypothesis (CH) from ZFC. This result is among the most outstanding achievements in 20th century mathematics. For this work Cohen was awarded the Fields Medal in 1966 and the National Medal of Science in 1967 the 1966 Fields Medal continues to be the only Fields Medal to have been awarded for a work in mathematical logic.