Mathematical Logic: Exercises and Solutions
暫譯: 數學邏輯：習題與解答
Csirmaz, Laszlo, Gyenis, Zalán
- 出版商: Springer
- 出版日期: 2022-03-15
- 售價: $2,990
- 貴賓價: 9.5 折 $2,841
- 語言: 英文
- 頁數: 312
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3030790096
- ISBN-13: 9783030790097
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商品描述
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– Fraïssé game; ultraproducts; and examples for axiomatizability and non-axiomatizability. The Arithmetic part covers Robinson’s theory, Peano’s axiom system, and Gödel’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 and topics 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 Gödel’s famous completeness and incompleteness theorems. Examples of applications on axiomatizability and decidability of numerous mathematical theories enrich this volume.
商品描述(中文翻譯)
這本書匯集了一系列色彩繽紛的經典數學邏輯問題，這些問題是從超過30年的教學中精選而來。最初的章節從支持性領域的問題開始，例如集合論（超濾子構造）、完全資訊博弈論（策略）、自動機和遞歸理論（可判定性、克萊尼定理）。接著，內容進一步探討命題邏輯（緊湊性和完備性、解析法），然後是第一階邏輯，包括量詞消除和Ehrenfeucht–Fraïssé遊戲；超積；以及公理化和非公理化的例子。算術部分涵蓋了羅賓遜理論、皮亞諾公理系統和哥德爾的不完備性定理。最後，書中觸及了普遍圖、錦標賽和數學邏輯中的零一法則。
教授數學邏輯的教師以及希望理解其概念和方法的學生，都能從這本書中獲益良多。書中的風格和主題特別選擇，使得對數學內容和方法感興趣的讀者能夠跟隨問題並自行證明主要定理，包括哥德爾著名的完備性和不完備性定理。關於多個數學理論的公理化和可判定性的應用範例，為本書增添了豐富的內容。
作者簡介
Laszlo Csirmaz is Senior Researcher at the Institute of Information Theory and Automation (UTIA), Czech Republic and Rényi Alfréd Institute of Mathematics. He started his career in 1975 at the Rényi Institute, where he co-founded the Cryptography Group. From 1996 to 2020, he was Chair of the Computer and Statistics Center at the Central European University, Hungary. Since 1990, he has been delivering lectures at the Eötvös Loránd University, Hungary, mainly on Set Theory and Mathematical Logic, and has held a part-time position at the University of Debrecen, Hungary, from 2001 to 2018.
Zalán Gyenis got his Ph.D. in Mathematics in 2013 from the Central European University, Hungary, and has been Premium Postdoctoral Research Fellow at the Hungarian Academy of Sciences. Since 2017, he has been working as Assistant Professor at the Logic Department of the Jagiellonian University, Poland. In 2018, he was awarded the Alfred Tarski Logic Prize.
作者簡介(中文翻譯)
Laszlo Csirmaz 是捷克共和國資訊理論與自動化研究所 (UTIA) 的高級研究員，以及 Rényi Alfréd 數學研究所的成員。他於1975年在 Rényi 研究所開始他的職業生涯，並共同創立了密碼學小組。從1996年到2020年，他擔任匈牙利中央歐洲大學計算機與統計中心的主任。自1990年以來，他在匈牙利厄爾特大學講授課程，主要涉及集合論和數學邏輯，並於2001年至2018年在匈牙利德布勒森大學擔任兼職職位。
Zalán Gyenis 於2013年在匈牙利中央歐洲大學獲得數學博士學位，並曾擔任匈牙利科學院的高級博士後研究員。自2017年以來，他在波蘭雅蓋隆大學邏輯系擔任助理教授。2018年，他獲得了阿爾弗雷德·塔斯基邏輯獎。
