| 书目名称 | Introduction to Incompleteness | | 副标题 | From Gödel‘s Theorem | | 编辑 | Serafim Batzoglou | | 视频video | | | 概述 | Provides a complete and accessible technical exposition of incompleteness to help overcome pedagogical challenges.Makes technically or conceptually difficult proofs more approachable with intuitive ex | | 图书封面 |  | | 描述 | .Incompleteness is a fascinating phenomenon at the intersection of mathematical foundations, computer science, and epistemology that places a limit on what is provable. However, despite its importance, it is often overlooked in the mathematics curricula because it is difficult to teach. This book aims to help bridge this pedagogical gap by providing a complete and accessible technical exposition of incompleteness for a wide audience. The author accomplishes this by making conceptually difficult proofs more approachable by providing intuitive explanations of the main ideas. Care is taken to emphasize the different layers of the mathematical argument – the layer .within. and the metalayer .about .an axiomatic system...Structurally, the book efficiently examines key results and arrives at some of the most interesting concepts as quickly as possible. It begins with Gödel‘s incompleteness theorems before continuing on to challenging concepts in the arithmetized completeness theorem, the Paris-Harrington theorem, and the independence of the continuum hypothesis. Other topics covered include the Lucas-Penrose arguments, ordinals and cardinals, and axiomatic set theory. Additionally, the a | | 出版日期 | Book 2024 | | 关键词 | Kurt Gödel; Gödel incompleteness theorems; Gödel completeness theorems; Mathematical incompleteness; Con | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-64217-3 | | isbn_softcover | 978-3-031-64219-7 | | isbn_ebook | 978-3-031-64217-3 | | 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 19:22:39
