Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics (Science Networks. Historical Studies) ebook

by Jose Ferreiros,Erwin Hiebert,Eberhard Knobloch,Erhard Scholz

Jose Ferreiros Erwin Hiebert Eberhard Knobloch Erhard Scholz Mathematics English

Authors: Ferreiros, Jose.

Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of Georg Cantor, it analyzes his work and the emergence of transfinite set theory within the broader context of the rise of modern mathematics. The text has a tripartite structure.

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Three case studies from elementary arithmetic show, informally, that there . The Early History of The Axiom of Choice.

Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. Medvedev, Fyodor . The Early History of The Axiom of Choice, Moscow: Nauka, 1982, (Russian). Zermelo's Axiom of Choice: Its Origins, Development, and Influence.

Ferreirós Domínguez, José. Set theory - History. Books for People with Print Disabilities. Basel ; Boston, MA. : BirkhäuserVerlag. inlibrary; printdisabled; trent university;. Trent University Library Donation. Internet Archive Books. Uploaded by station03. cebu on July 9, 2019. SIMILAR ITEMS (based on metadata). Terms of Service (last updated 12/31/2014).

Categories: Mathematics.

Mathematics and Its History.

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Labyrinth of Thought, by José Ferreirrós, published this year in its second revised . Thereafter the book’s Part Three addresses the further evolution of se. .

Ferreirós makes his case via a two-pronged analysis: Part One of Labyrinth of Thought concerns the way in which crypto-set theory answered the indicated calls from algebra, arithmetic, and geometry; Part Two then addresses Cantor’s work on infinity and the continuum with Dedekind also cast in a major role

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Kecq

This is maybe the best book about the subject. The author not only traces the mathematical roots of the new discoveries, showing like no other has done the relationships with the mathematics of the beginning of the XIX century, but he also gives a detailed, and very vivid, description of the characters of the people involved. (Maybe the best part is where he describes the correspondence between Cantor and Dedekind). But there should be a paperback version, for people like me, living in Colombia, the price is terribly high. Even in Spain, where the author comes from, it is inaccesible. There also should be a spanish version (there was one previous version in spanish, but now it is out of the market).

Winasana

of the complex origins and development of set theory. Riemann's

important role in the early stages of this history are detailled,

as well as Cantor's better known contributions. Fundamental to

any study of this topic.