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Can mathematics be proved consistent...

Godel, Kurt.

Can mathematics be proved consistent?Godel's shorthand notes & lectures on incompleteness /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Can mathematics be proved consistent?by Jan von Plato.
其他題名:	Godel's shorthand notes & lectures on incompleteness /
作者:	Von Plato, Jan.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	ix, 263 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Godel's theoremHistory.
電子資源:	https://doi.org/10.1007/978-3-030-50876-0
ISBN:	9783030508760$q(electronic bk.)

Can mathematics be proved consistent?Godel's shorthand notes & lectures on incompleteness /
Von Plato, Jan.

Can mathematics be proved consistent?Godel's shorthand notes & lectures on incompleteness /[electronic resource] :by Jan von Plato. - Cham :Springer International Publishing :2020. - ix, 263 p. :ill., digital ;24 cm. - Sources and studies in the history of mathematics and physical sciences,2196-8810. - Sources and studies in the history of mathematics and physical sciences..

I. Godel'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.

Kurt Godel (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. Godel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren't. The result is known as Godel's 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 Godel's 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 Godel's incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Godel 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.

ISBN: 9783030508760$q(electronic bk.)

Standard No.: 10.1007/978-3-030-50876-0doiSubjects--Personal Names:

874476
Godel, Kurt.
Subjects--Topical Terms:

874477
Godel's theorem
--History.

LC Class. No.: QA9.65 / .V667 2020

Dewey Class. No.: 511.3

Can mathematics be proved consistent?Godel's shorthand notes & lectures on incompleteness /
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