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Kurt Godelthe Princeton lectures on ...

Hameen-Anttila, Maria.

Kurt Godelthe Princeton lectures on intuitionism /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Kurt Godeledited by Maria Hameen-Anttila, Jan von Plato.
其他題名:	the Princeton lectures on intuitionism /
其他作者:	Hameen-Anttila, Maria.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	ix, 133 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Godel's theorem.
電子資源:	https://doi.org/10.1007/978-3-030-87296-0
ISBN:	9783030872960$q(electronic bk.)

Kurt Godelthe Princeton lectures on intuitionism /
Kurt Godelthe Princeton lectures on intuitionism /[electronic resource] :edited by Maria Hameen-Anttila, Jan von Plato. - Cham :Springer International Publishing :2021. - ix, 133 p. :ill., digital ;24 cm. - Sources and studies in the history of mathematics and physical sciences,2196-8829. - Sources and studies in the history of mathematics and physical sciences..

Godel's Functional Interpretation in Context -- Part I: Axiomatic Intuitionist Logic -- Part II: The Functional Interpretation -- References -- Name Index.

Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Godel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Godel's incompleteness theorem. Godel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Godel. The second is a problem still wide open. Godel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Godel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Godel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.

ISBN: 9783030872960$q(electronic bk.)

Standard No.: 10.1007/978-3-030-87296-0doiSubjects--Topical Terms:

665760
Godel's theorem.

LC Class. No.: QA9.65 / .G2 2021

Dewey Class. No.: 511.3

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