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|a 10.1007/978-3-030-87296-0
|2 doi
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|a (OCoLC)1290021778
|z (OCoLC)1289340764
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|b Springer
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|a MAT015000
|2 bisacsh
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|a HCDD
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1 |
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|a Gödel, Kurt.
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|a Kurt Gödel :
|b The Princeton lectures on intuitionism /
|c Maria Hämeen-Anttila, Jan von Plato, editors.
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| 260 |
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|a Cham, Switzerland :
|b Springer,
|c 2021.
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| 300 |
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|a 1 online resource (141 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|b PDF
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|a text file
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|a Sources and studies in the history of mathematics and physical sciences
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|a 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.
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|a Includes bibliographical references and index.
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|a Online resource; title from PDF title page (SpringerLink, viewed January 19, 2022).
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|a Gödel's Functional Interpretation in Context -- Part I: Axiomatic Intuitionist Logic -- Part II: The Functional Interpretation -- References -- Name Index.
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| 650 |
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|a Gödel's theorem.
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| 650 |
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|a Teorema de Gödel
|2 embne
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|a Gödel's theorem
|2 fast
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|a Hämeen-Anttila, Maria.
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1 |
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|a Von Plato, Jan.
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| 758 |
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|i has work:
|a Kurt Gödel (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGDBJtpB9KK7QFRqPjvyMK
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
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|i Print version:
|a Hämeen-Anttila, Maria
|t Kurt Gödel
|d Cham : Springer International Publishing AG,c2022
|z 9783030872953
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| 830 |
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|a Sources and studies in the history of mathematics and physical sciences.
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| 856 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-030-87296-0
|y Click for online access
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| 880 |
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|6 505-00/(S
|a Intro -- Preface -- Acknowledgements -- Contents -- Introduction: Gödel's functional interpretation in context -- Content of the lectures -- Sources -- The intuitionistic viewpoint -- Between intuitionistic and classical logic -- Vagueness and absurdity: Gödel's critique of intuitionism -- The constructive system Σ and the calculability question -- Interpretation of intuitionistic arithmetic in system E -- Applications of the E-translation -- After the seventeen-year silence -- Princeton Lectures on Intuitionism -- Notebook 1 -- Notebook 2
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|a SPRING-MATH2021
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|a 92
|b HCD
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