| 书目名称 | Kurt Gödel | | 副标题 | The Princeton Lectur | | 编辑 | Maria Hämeen-Anttila,Jan von Plato | | 视频video | | | 概述 | Offers indispensable reading for mathematicians and computer scientists.Gives insights into thework that is needed to solve scientific questions.Forms a basis for further investigations into Gödel‘s v | | 丛书名称 | Sources and Studies in the History of Mathematics and Physical Sciences | | 图书封面 |  | | 描述 | 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 Gödel, a logical icon of that time, showed Hilbert‘s ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel‘s .incompleteness theorem.. Gödel 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 Gödel. The second is a problem still wide open. Gödel 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, Gödel‘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. I | | 出版日期 | Book 2021 | | 关键词 | axiomatic intuitionistic logic; properties of partial recursive functions; Heyting arithmetic; Arbeitsh | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-87296-0 | | isbn_softcover | 978-3-030-87298-4 | | isbn_ebook | 978-3-030-87296-0Series ISSN 2196-8810 Series E-ISSN 2196-8829 | | issn_series | 2196-8810 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:46:34
