Mathematical Logic 在线电子书 图书标签: 逻辑学 数理逻辑 数学 英文原版 logic Math 教科书 MathLogic
发表于2025-03-04
Mathematical Logic 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2025
做了本科生数理逻辑的助教,这本是教材,写得足够清晰,但总感觉有些概念的引入,比如树,对于刚入门的学生来说不是很必要。总体而言是入门的好书,但最好有素朴集合论基础。
评分大一的时候数理逻辑课的教材
评分作为入门,讲解挺清晰,习题难度适中
评分做了本科生数理逻辑的助教,这本是教材,写得足够清晰,但总感觉有些概念的引入,比如树,对于刚入门的学生来说不是很必要。总体而言是入门的好书,但最好有素朴集合论基础。
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Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
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Mathematical Logic 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2025