| 書(shū)目名稱(chēng) | Mathematical Logic | | 副標(biāo)題 | Exercises and Soluti | | 編輯 | Laszlo Csirmaz,Zalán Gyenis | | 視頻video | http://file.papertrans.cn/627/626204/626204.mp4 | | 概述 | Offers a broad set of problems in Mathematical Logic, starting from its supporting fields and advancing toward key theorems.Enables the student to prove the main theorems himself, including G?del‘s fa | | 叢書(shū)名稱(chēng) | Problem Books in Mathematics | | 圖書(shū)封面 |  | | 描述 | .This book gathers together a colorful set of problems on classical Mathematical Logic, selected from over 30 years of teaching. The initial chapters start with problems from supporting fields, like set theory (ultrafilter constructions), full-information game theory (strategies), automata, and recursion theory (decidability, Kleene’s theorems). The work then advances toward propositional logic (compactness and completeness, resolution method), followed by first-order logic, including quantifier elimination and the Ehrenfeucht– Fra?ssé game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson’s theory, Peano’s axiom system, and G?del’s incompleteness theorems. Finally, the book touches universal graphs, tournaments, and the zero-one law in Mathematical Logic..Instructors teaching Mathematical Logic, as well as students who want to understand its concepts and methods, can greatly benefit from this work. The style andtopics have been specially chosen so that readers interested in the mathematical content and methodology could follow the problems and prove the main theorems themselves, including G?del’s famous completeness and | | 出版日期 | Textbook 2022 | | 關(guān)鍵詞 | mathematical logic; formal logic; first-order logic; propositional calculus; predicate calculus; G?del’s | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-79010-3 | | isbn_softcover | 978-3-030-79012-7 | | isbn_ebook | 978-3-030-79010-3Series ISSN 0941-3502 Series E-ISSN 2197-8506 | | issn_series | 0941-3502 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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