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000938773 019__ $$a1178998138
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000938773 0247_ $$a10.1007/978-3-030-50876-0$$2doi
000938773 0247_ $$a10.1007/978-3-030-50
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000938773 050_4 $$aQA9.65
000938773 08204 $$a511.3$$223
000938773 1001_ $$aVon Plato, Jan.
000938773 24510 $$aCan mathematics be proved consistent? :$$bGödel's shorthand notes & lectures on incompleteness /$$cJan von Plato.
000938773 260__ $$aCham :$$bSpringer,$$c2020.
000938773 300__ $$a1 online resource
000938773 336__ $$atext$$btxt$$2rdacontent
000938773 337__ $$acomputer$$bc$$2rdamedia
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000938773 4901_ $$aSources and studies in the history of mathematics and physical sciences
000938773 504__ $$aIncludes bibliographical references and index.
000938773 5050_ $$aI. Gödel's Steps Toward Incompleteness -- II. The Saved Sources on Incompleteness -- III. The Shorthand Notebooks -- IV. The Typewritten Manuscripts -- V. Lectures and Seminars on Incompleteness -- Index -- References.
000938773 506__ $$aAccess limited to authorized users.
000938773 520__ $$aKurt Gödel (1906-1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but arent. The result is known as Gödels first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?" This book offers the first examination of Gödels preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was composed.The book also contains the original version of Gödels incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.
000938773 60010 $$aGödel, Kurt.
000938773 650_0 $$aGödel's theorem$$xHistory.
000938773 650_0 $$aMathematics$$xHistory.
000938773 77608 $$iPrint version: $$z3030508757$$z9783030508753$$w(OCoLC)1154985680
000938773 830_0 $$aSources and studies in the history of mathematics and physical sciences.
000938773 852__ $$bebk
000938773 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-50876-0$$zOnline Access$$91397441.1
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