Richard Hodel:《数理逻辑导论》中推荐的参考书
Richard Hodel:《数理逻辑导论》中推荐的参考书
【说明】:
Richard Hodel的《An Introduction to Mathematical Logic》的书末,给出了一份数理逻辑的参考书和阅读清单,个人觉得很有代表性,基本上覆盖了本书的主要话题并列出了关于同一话题的各家之言。
这个推荐书单,分为8部分:
第一部分:数理逻辑的标准教科书,覆盖了模型论、证明论的内容
第二部分:递归论可计算性的标准教科书
第三部分:集合论的经典教科书
第四部分:希尔伯特第十问题的论文和科普教科书
第五部分:数学哲学、符号逻辑、数理逻辑、哥德尔定理的科普读物,这部分、入门或者背景性书籍比较多
第六部分:数理逻辑史上几篇(和本教科书有关的)重要论文
第七部分:专题文章
第八部分:数论教科书
如果书单中的书籍有中文版,只收录中文版,否则则是英文版。这些书,你没有必要读过,只要知道书名就可以,也算是扩大知识面。以后当你需要某方面知识时知道哪些书是必读,哪些是参考,哪些是名著。列出书单的主要目的是开阔视野,为你自学提供各种不同程度的参考资料,也为在读研究生和数理逻辑爱好者提供数理逻辑方面的资源指南。每本书都给出了该书在豆瓣的主页链接。虽然相当部分的英文书籍的主页没有介绍,但本人会在时间许可的情况下逐步更新。建立这个书单时,一部分图书豆瓣本没有条目,本人现在已经全部添加,保证每本书都有豆瓣链接。但是论文部分因历史久远,又包含在专业杂志中,很难找到直接的拷贝,目前没有链接。
【数理逻辑全般】:
书名:An Introduction to Mathematical Logic and Type Theory: To Truth through Proof
作者:Peter B. Andrews
书名:The Language of First-Order Logic
作者:Jon Barwise and John Etchemendy
书名:A Course in Mathematical Logic
作者:John Bell and Moshé
书名:The Unprovability of Consistency: An Essay in Modal Logic
作者:George S. Boolos
书名:Computability and Logic (5th edition)
作者:George S. Boolos and Richard C. Jeffrey
书名:Model Theory
作者:C. C. Chang & H. J. Keisler
书名:Mathematical Intuitionism
作者:A. G. Draglin
书名:数理逻辑
作者:H. D. Ebbinhous and J. Flum and W. Thomas
书名:数理逻辑
作者:Herbert Enderton
书名:First-Order Logic and Automated Theorem Proving
作者:Melvin Fitting
书名:Logic for Computer Science
作者:Jean H. Gallier
书名:Logic for Mathematicians
作者:A. G. Hamilton
书名:Introduction to Metamathematics
作者:Stephen C. Kleene
书名:Notes on Logic
作者:Roger C. Lyndon
书名:Introduction to Mathematical Logic
作者:Jerome Malitz
书名:First-Order Mathematical Logic
作者:Angelo Margaris
书名:Elementary Logic
作者:Benson Mates
书名:数理逻辑
作者:Elliot Mendelson
书名:Mathematical Logic
作者:Donald J. Monk
书名:应用逻辑
作者:Anil Nerode and Richard A. Shore
书名:Logic for Computer Scientists
作者:Uwe Schöning
书名:Mathematical Logic
作者:Joseph. R. Shoenfield
书名:From Symbolic Logic … to Mathematical Logic
作者:Charles L. Silver
书名:哥德尔不完全性定理
作者:Raymond M. Smullyan
书名:First-Order Logic
作者:Raymond M. Smullyan
书名:A Survey of Mathematical Logic
作者:Hao Wang (王浩)
【递归论与可计算性】
书名:Computability
作者:Nigel J. Cutland
书名:Computability and Unsolvability
作者:Martin Davis
书名:The Undecidable
作者:Martin Davis
书名:Computability: Computable Functions, Logic, and Foundations of Mathematics
作者:Richard L. Epstein and Walter A. Carnielli
书名:Introduction to Computation Theory
作者:Richard G. Hamlet
书名:Introduction to Computability
作者:Fredrick Hennie
书名:Elements of the Theory of Computation
作者:Harry R. Lewis and Christos H. Papadimitriou
书名:A Programming Approach to Computability
作者:A. J. Kfoury and Rober N. Moll and Michael A. Arbib
书名:An Introduction to the General Theory of Algorithms
作者:Michael Machtey and Paul Young
书名:Computation: Finite and Infinite Machines
作者:Marvin Minsky
书名:An Introduction to Formal Language Theory
作者:Robert N. Moll and Michael A. Arbib and A. J. Kfoury
书名:Classical Recursion Theory
作者:P. Odifreddi
书名:Theory of Recursive Functions and Effective Computability
作者:Hartley Rogers
书名:Recursion Theory
作者:J. R. Shoenfield
书名:Recursion Theory for Metamathematicians
作者:Raymond M. Smullyan
书名:Recursively Enumerable Sets and Degrees
作者:Robert Soare
书名:Theory of Computation
作者:George Tourlakis
书名:Recursive Function Theory and Logic
作者:Ann Yasuhara
【集合论】:
书名:Set theory and the Continuum Hypothesis
作者:Paul J. Cohen
书名:Foundations of Set Theory
作者:Abraham A. Frankel and Yehoshua Bar-Hillel
书名:Set Theory: An Introduction to Independence Proofs
作者:Kenneth Kunen
书名:集合论
作者:Thomas Jech
书名:Introduction to Set Theory (3rd edition)
作者:Karel Hrbacek and Thomas Jech
书名:Notes on Logic and Set Theory
作者:P. T. Johnstone
书名:Introduction to Modern Set Theory
作者:Judith Roitman
书名:Sets: Naive, Axiomatic and Applied
作者:D. Van Dalen and H. C. Doets and H. de Swart
书名:Set Theory
作者:Robert L. Vaught
【希尔伯特第十问题】:
书名:Computability and Logic
作者:Daniel E Cohen
论文名:Hilbert’s tenth problem is unsolvable
作者:Martin Davis
出处:American Math Monthly 80(1973), 233-269
论文名:Hilbert’s Tenth Program. Diophantine Equations: Positive Aspects of a Negative Solution
作者:Martin D. Davis and Yuri V. Matiyasevich and Julia Robinson
出处:Proceedings of Symposia in Pure Mathematics 28(1976). Providence, RI: Am. Math. Soc., 323-378
论文名:The Decision problem for exponential Diophantine equations
作者:Martin Davis and Hilary Putnam and Julia Robinson
出处:Annals of Mathematics 74(1961) 425-436
论文名:Proof of Recursive Unsolvability of Hilbert’s Tenth Problem
作者:J. P. Jones and Yuri Matiyasevich
出处:American Math Monthly 98(1991) 689-709
书名:A Course in Mathematical Logic
作者:Yu I. Manin
论文名:Enumerable sets are Diophatine
作者:Yuri Matiyasevich
出处:Soviet Math. Dokl. 11(1970)
书名:Hilbert’s 10th Problem
作者:Yuri Matiyasevich
论文名:Hilbert’s Tenth Problem
作者:Julia Robinson
出处:Proceedings of Symposia in Pure Mathematics 20(1969), 191-194
Julia Robinson and Hilbert's Tenth Problem
书名:Logical Number Theory
作者:Craig Smoryński
【符号逻辑、数学哲学、哥德尔定理科普】:
书名:Philosophy of Mathematics: Selected Readings (2nd edition)
作者:Paul Benacerraf and Hilary Putnam
书名:Symbolic Logic
作者:Lewis Carroll
书名:Symbolic Logic
作者:Irving Copi
书名:A Profile of Mathematical Logic
作者:Howard DeLong
书名:Proof, Logic and Formalization
作者:Michael Detlefsen
书名:Numbers, Sets, and Axioms
作者:A. G. Hamilton
书名:The Universal Turing Machine
作者:Rolf Herken
书名:哥德尔、艾舍尔、巴赫:集异璧之大成
作者:侯士达
书名:数学:确定性的丧失
作者:Morris Kline
书名:If P, Then Q: Conditionals and the Foundations of Reasoning
作者:David H. Sanford
书名:Gödel’s Theorem in Focus
作者:S. G. Shanker
书名:The Lady or the Tiger?
作者:Raymond M. Smullyan
书名:Forever Undecided
作者:Raymond M. Smullyan
书名:From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931
作者:Jean Van Heijenoort
书名:数理逻辑通俗讲话
作者:王浩
书名:哥德尔(Reflections on Kurt Gödel)
作者:王浩
【数论】:
书名:Elementary Number Theory (revised edition)
作者:David M. Burton
书名:Elementary Number Theory and its Applications (6th edition)
作者:Kenneth Rosen
【著名论文】:
论文名:Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme
出处:Monatschefte für Mathematik und Phzsik 38(1931), 173-198
书名:On formally undecidable propositions of Principia Mathematica and related systems
作者:Kurt Gödel
论文名:General recursive functions of natural numbers
作者:Stephen C. Kleene
出处:Math. Ann. 112(1936), 727-742
论文名:Recursively enumerable sets of positive integers and their decision problems
作者:Emil Post
出处:Bulletin American Math. Society 50(1944), 284-316
论文名:Computability of recursive functions
作者:J. C. Shepherdson and H. E. Sturgis
出处:Comp. Mach. 10(1963), 217-255
论文名:On computable numbers, with an application to the Entscheidungsproblem
作者:Alan Turing
出处:Proceedings of the London Mathematical Society, ser. 2, 42(1936) 230-265
【专题论文】:
论文名:Hypersets
作者:Jon Barwise and Larry Moss
出处:Mathematical Intelligencer 13(1991) New York: Springer-Verlag, 31-41
论文名:Unsolvable Problems
作者:Martin Davis
出处:《Handbook of Mathematical Logic》
论文名:Algorithms and Decision Problems: A Crash Course in Recursion Theory
作者:Dirk Van Dalen
出处:《Handbook of Philosophical Logic Volume I》
论文名:On the Infinite
作者:David Hilbert
出处:《From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931》
论文名:Elementary Predicate Logic
作者:Wilfrid Hodges
出处:《Handbook of Philosophical Logic Volume I》
论文名:Axioms of Set Theory
作者:J. R. Shoenfield
出处:《Handbook of Mathematical Logic》
论文名:Systems of Deduction
作者:Göran Sundholm
出处:《Handbook of Philosophical Logic Volume I》
论文名:Hibert’s Programme
作者:Craig Smoryński
出处:CWI Quartly 1(1988), 3-59
论文名:Gödel’s and Some Other Examples of Problem Transmutation
作者:Hao Wang (王浩)
出处:《Perspectives on the History of Mathematical Logic》
【说明】:
Richard Hodel的《An Introduction to Mathematical Logic》的书末,给出了一份数理逻辑的参考书和阅读清单,个人觉得很有代表性,基本上覆盖了本书的主要话题并列出了关于同一话题的各家之言。
这个推荐书单,分为8部分:
第一部分:数理逻辑的标准教科书,覆盖了模型论、证明论的内容
第二部分:递归论可计算性的标准教科书
第三部分:集合论的经典教科书
第四部分:希尔伯特第十问题的论文和科普教科书
第五部分:数学哲学、符号逻辑、数理逻辑、哥德尔定理的科普读物,这部分、入门或者背景性书籍比较多
第六部分:数理逻辑史上几篇(和本教科书有关的)重要论文
第七部分:专题文章
第八部分:数论教科书
如果书单中的书籍有中文版,只收录中文版,否则则是英文版。这些书,你没有必要读过,只要知道书名就可以,也算是扩大知识面。以后当你需要某方面知识时知道哪些书是必读,哪些是参考,哪些是名著。列出书单的主要目的是开阔视野,为你自学提供各种不同程度的参考资料,也为在读研究生和数理逻辑爱好者提供数理逻辑方面的资源指南。每本书都给出了该书在豆瓣的主页链接。虽然相当部分的英文书籍的主页没有介绍,但本人会在时间许可的情况下逐步更新。建立这个书单时,一部分图书豆瓣本没有条目,本人现在已经全部添加,保证每本书都有豆瓣链接。但是论文部分因历史久远,又包含在专业杂志中,很难找到直接的拷贝,目前没有链接。
【数理逻辑全般】:
书名:An Introduction to Mathematical Logic and Type Theory: To Truth through Proof
作者:Peter B. Andrews
书名:The Language of First-Order Logic
作者:Jon Barwise and John Etchemendy
书名:A Course in Mathematical Logic
作者:John Bell and Moshé
书名:The Unprovability of Consistency: An Essay in Modal Logic
作者:George S. Boolos
书名:Computability and Logic (5th edition)
作者:George S. Boolos and Richard C. Jeffrey
书名:Model Theory
作者:C. C. Chang & H. J. Keisler
书名:Mathematical Intuitionism
作者:A. G. Draglin
书名:数理逻辑
作者:H. D. Ebbinhous and J. Flum and W. Thomas
书名:数理逻辑
作者:Herbert Enderton
书名:First-Order Logic and Automated Theorem Proving
作者:Melvin Fitting
书名:Logic for Computer Science
作者:Jean H. Gallier
书名:Logic for Mathematicians
作者:A. G. Hamilton
书名:Introduction to Metamathematics
作者:Stephen C. Kleene
书名:Notes on Logic
作者:Roger C. Lyndon
书名:Introduction to Mathematical Logic
作者:Jerome Malitz
书名:First-Order Mathematical Logic
作者:Angelo Margaris
书名:Elementary Logic
作者:Benson Mates
书名:数理逻辑
作者:Elliot Mendelson
书名:Mathematical Logic
作者:Donald J. Monk
书名:应用逻辑
作者:Anil Nerode and Richard A. Shore
书名:Logic for Computer Scientists
作者:Uwe Schöning
书名:Mathematical Logic
作者:Joseph. R. Shoenfield
书名:From Symbolic Logic … to Mathematical Logic
作者:Charles L. Silver
书名:哥德尔不完全性定理
作者:Raymond M. Smullyan
书名:First-Order Logic
作者:Raymond M. Smullyan
书名:A Survey of Mathematical Logic
作者:Hao Wang (王浩)
【递归论与可计算性】
书名:Computability
作者:Nigel J. Cutland
书名:Computability and Unsolvability
作者:Martin Davis
书名:The Undecidable
作者:Martin Davis
书名:Computability: Computable Functions, Logic, and Foundations of Mathematics
作者:Richard L. Epstein and Walter A. Carnielli
书名:Introduction to Computation Theory
作者:Richard G. Hamlet
书名:Introduction to Computability
作者:Fredrick Hennie
书名:Elements of the Theory of Computation
作者:Harry R. Lewis and Christos H. Papadimitriou
书名:A Programming Approach to Computability
作者:A. J. Kfoury and Rober N. Moll and Michael A. Arbib
书名:An Introduction to the General Theory of Algorithms
作者:Michael Machtey and Paul Young
书名:Computation: Finite and Infinite Machines
作者:Marvin Minsky
书名:An Introduction to Formal Language Theory
作者:Robert N. Moll and Michael A. Arbib and A. J. Kfoury
书名:Classical Recursion Theory
作者:P. Odifreddi
书名:Theory of Recursive Functions and Effective Computability
作者:Hartley Rogers
书名:Recursion Theory
作者:J. R. Shoenfield
书名:Recursion Theory for Metamathematicians
作者:Raymond M. Smullyan
书名:Recursively Enumerable Sets and Degrees
作者:Robert Soare
书名:Theory of Computation
作者:George Tourlakis
书名:Recursive Function Theory and Logic
作者:Ann Yasuhara
【集合论】:
书名:Set theory and the Continuum Hypothesis
作者:Paul J. Cohen
书名:Foundations of Set Theory
作者:Abraham A. Frankel and Yehoshua Bar-Hillel
书名:Set Theory: An Introduction to Independence Proofs
作者:Kenneth Kunen
书名:集合论
作者:Thomas Jech
书名:Introduction to Set Theory (3rd edition)
作者:Karel Hrbacek and Thomas Jech
书名:Notes on Logic and Set Theory
作者:P. T. Johnstone
书名:Introduction to Modern Set Theory
作者:Judith Roitman
书名:Sets: Naive, Axiomatic and Applied
作者:D. Van Dalen and H. C. Doets and H. de Swart
书名:Set Theory
作者:Robert L. Vaught
【希尔伯特第十问题】:
书名:Computability and Logic
作者:Daniel E Cohen
论文名:Hilbert’s tenth problem is unsolvable
作者:Martin Davis
出处:American Math Monthly 80(1973), 233-269
论文名:Hilbert’s Tenth Program. Diophantine Equations: Positive Aspects of a Negative Solution
作者:Martin D. Davis and Yuri V. Matiyasevich and Julia Robinson
出处:Proceedings of Symposia in Pure Mathematics 28(1976). Providence, RI: Am. Math. Soc., 323-378
论文名:The Decision problem for exponential Diophantine equations
作者:Martin Davis and Hilary Putnam and Julia Robinson
出处:Annals of Mathematics 74(1961) 425-436
论文名:Proof of Recursive Unsolvability of Hilbert’s Tenth Problem
作者:J. P. Jones and Yuri Matiyasevich
出处:American Math Monthly 98(1991) 689-709
书名:A Course in Mathematical Logic
作者:Yu I. Manin
论文名:Enumerable sets are Diophatine
作者:Yuri Matiyasevich
出处:Soviet Math. Dokl. 11(1970)
书名:Hilbert’s 10th Problem
作者:Yuri Matiyasevich
论文名:Hilbert’s Tenth Problem
作者:Julia Robinson
出处:Proceedings of Symposia in Pure Mathematics 20(1969), 191-194
Julia Robinson and Hilbert's Tenth Problem
书名:Logical Number Theory
作者:Craig Smoryński
【符号逻辑、数学哲学、哥德尔定理科普】:
书名:Philosophy of Mathematics: Selected Readings (2nd edition)
作者:Paul Benacerraf and Hilary Putnam
书名:Symbolic Logic
作者:Lewis Carroll
书名:Symbolic Logic
作者:Irving Copi
书名:A Profile of Mathematical Logic
作者:Howard DeLong
书名:Proof, Logic and Formalization
作者:Michael Detlefsen
书名:Numbers, Sets, and Axioms
作者:A. G. Hamilton
书名:The Universal Turing Machine
作者:Rolf Herken
书名:哥德尔、艾舍尔、巴赫:集异璧之大成
作者:侯士达
书名:数学:确定性的丧失
作者:Morris Kline
书名:If P, Then Q: Conditionals and the Foundations of Reasoning
作者:David H. Sanford
书名:Gödel’s Theorem in Focus
作者:S. G. Shanker
书名:The Lady or the Tiger?
作者:Raymond M. Smullyan
书名:Forever Undecided
作者:Raymond M. Smullyan
书名:From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931
作者:Jean Van Heijenoort
书名:数理逻辑通俗讲话
作者:王浩
书名:哥德尔(Reflections on Kurt Gödel)
作者:王浩
【数论】:
书名:Elementary Number Theory (revised edition)
作者:David M. Burton
书名:Elementary Number Theory and its Applications (6th edition)
作者:Kenneth Rosen
【著名论文】:
论文名:Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme
出处:Monatschefte für Mathematik und Phzsik 38(1931), 173-198
书名:On formally undecidable propositions of Principia Mathematica and related systems
作者:Kurt Gödel
论文名:General recursive functions of natural numbers
作者:Stephen C. Kleene
出处:Math. Ann. 112(1936), 727-742
论文名:Recursively enumerable sets of positive integers and their decision problems
作者:Emil Post
出处:Bulletin American Math. Society 50(1944), 284-316
论文名:Computability of recursive functions
作者:J. C. Shepherdson and H. E. Sturgis
出处:Comp. Mach. 10(1963), 217-255
论文名:On computable numbers, with an application to the Entscheidungsproblem
作者:Alan Turing
出处:Proceedings of the London Mathematical Society, ser. 2, 42(1936) 230-265
【专题论文】:
论文名:Hypersets
作者:Jon Barwise and Larry Moss
出处:Mathematical Intelligencer 13(1991) New York: Springer-Verlag, 31-41
论文名:Unsolvable Problems
作者:Martin Davis
出处:《Handbook of Mathematical Logic》
论文名:Algorithms and Decision Problems: A Crash Course in Recursion Theory
作者:Dirk Van Dalen
出处:《Handbook of Philosophical Logic Volume I》
论文名:On the Infinite
作者:David Hilbert
出处:《From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931》
论文名:Elementary Predicate Logic
作者:Wilfrid Hodges
出处:《Handbook of Philosophical Logic Volume I》
论文名:Axioms of Set Theory
作者:J. R. Shoenfield
出处:《Handbook of Mathematical Logic》
论文名:Systems of Deduction
作者:Göran Sundholm
出处:《Handbook of Philosophical Logic Volume I》
论文名:Hibert’s Programme
作者:Craig Smoryński
出处:CWI Quartly 1(1988), 3-59
论文名:Gödel’s and Some Other Examples of Problem Transmutation
作者:Hao Wang (王浩)
出处:《Perspectives on the History of Mathematical Logic》
看到现在就觉得殷海光的逻辑新引最通俗易懂,其他看的真心头大
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