| 书目名称 | The Code of Mathematics | | 副标题 | Proof and Truth | | 编辑 | Stefan Müller-Stach | | 视频video | | | 概述 | Introduction into fundamental concepts of mathematics.Explains the main three foundations of mathematics: set theory, category theory and homotopy type theory.Depicts the motivation behind homotopy ty | | 丛书名称 | Mathematics Study Resources | | 图书封面 |  | | 描述 | .Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants...This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.. | | 出版日期 | Textbook 2024 | | 关键词 | Univalent Foundations; Martin Löf; type theory; equivalence; homotopy type theory; incompleteness; truth; V | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-69483-1 | | isbn_softcover | 978-3-662-69482-4 | | isbn_ebook | 978-3-662-69483-1Series ISSN 2731-3824 Series E-ISSN 2731-3832 | | issn_series | 2731-3824 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE |
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发表于 2025-3-21 18:56:48
