| 書(shū)目名稱(chēng) | The Code of Mathematics | | 副標(biāo)題 | Proof and Truth | | 編輯 | Stefan Müller-Stach | | 視頻video | http://file.papertrans.cn/907/906317/906317.mp4 | | 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 | | 叢書(shū)名稱(chēng) | Mathematics Study Resources | | 圖書(shū)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 G?del 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 | | 關(guān)鍵詞 | Univalent Foundations; Martin L?f; 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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