Introduction to Mathematical Logic (Discrete Mathematics and Its Applications) 6th Edition by Elliott Mendelson (PDF)

Description

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.The sixth edition incorporates recent work on Gödel’s second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

User’s Reviews

Editorial Reviews: Review Praise for the Fifth Edition”Since it first appeared in 1964, Mendelson’s book has been recognized as an excellent textbook in the field … This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with.”―Computing Reviews”Since its first edition, this fine book has been a text of choice for a beginner’s course on mathematical logic … There are many fine books on mathematical logic, but Mendelson’s textbook remains a sure choice for a first course for its clear explanations and organization…”―MAA Reviews”[This book] is the most concise and readable introductory text I have ever encountered … I have pulled the ideas for many test questions from it over the years.”―Charles Ashbacher, Upper Iowa UniversityPraise for the Fifth Edition”Since it first appeared in 1964, Mendelson’s book has been recognized as an excellent textbook in the field. It is one of the most frequently mentioned texts in references and recommended reading lists … This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with.”―Computing Reviews, May 2010″The following are the significant changes in this edition: A new section (3.7) on the order type of a countable nonstandard model of arithmetic; a second appendix, Appendix B, on basic modal logic, in particular on the normal modal logics K, T, S4, and S5 and the relevant Kripke semantics for each; an expanded bibliography and additions to both the exercises and to the Answers to Selected Exercises, including corrections to the previous version of the latter.”―J.M. Plotkin, Zentralblatt MATH 1173″Since its first edition, this fine book has been a text of choice for a beginner’s course on mathematical logic. … There are many fine books on mathematical logic, but Mendelson’s textbook remains a sure choice for a first course for its clear explanations and organization: definitions, examples and results fit together in a harmonic way, making the book a pleasure to read. The book is especially suitable for self-study, with a wealth of exercises to test the reader’s understanding.”―MAA Reviews, December 2009 About the Author Elliott Mendelson is professor emeritus at Queens College in Flushing, New York, USA. Dr. Mendelson obtained his bachelor’s degree at Columbia University and his master’s and doctoral degrees at Cornell University, and was elected afterward to the Harvard Society of Fellows. In addition to his other writings, he is the author of another CRC Press book Introducing Game Theory and Its Applications.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Before reading this text, my background with mathematical logic is limited to an undergrad “Intro to Mathematical Proofs” course required for math majors before taking analysis, topology, and modern algebra courses. It covered the basic propositional and predicate calculus, but went no further than its immediate application to elementary mathematical proof. In this sense, I am a beginner when it comes to the formal study of Mathematical Logic, and I have had some great experiences reading this book as a self-study text.This book has been an excellent text for self study, thus far. This book contains five total chapters: the first two contain the fundamental theorems of First-Order Logic, the third covers an axiomatic number theory and Godel’s incompleteness theorems, the fourth discusses axiomatic set theory, and the fifth serves as an introduction to computability theory. I planned on a detailed study of the first three chapters before moving on to a different text on Axiomatic Set Theory, and have just finished the first chapter.Despite what another reviewer has said about the text, I have found the material in this chapter to be quite accessible. The material in this chapter is self contained, in that you can begin right away with Mendelson’s definitions at the beginning of each section and proceed to prove all of the presented theorems using those definitions. No prior experience with propositional logic is needed when beginning chapter 1, since it takes an axiomatic approach. Skip none of the exercises, and leave no lemma, proposition, or theorem unproven. There is valuable experience gained in completing all of these on your own. I highly recommend this text for self study.

⭐I don’t like this book. Here are the reasons:1) How could the subscript font still be so unreadable – this is the 6th edition. The”i” and “j” subscripts are nearly impossible to decipher.2) The material in this book in dense and each page requires several re-reads to gain a clear understanding. This is true in most advanced Mathematics, but it seems unnecessarily complicated. A much clearer book is Hamilton’s “Logic for Mathematicians”.https://www.amazon.com/Logic-Mathematicians-G-Hamilton/dp/05213686503) The book has plenty of problems, and provides some complete answers in the back of the book. But, it doesn’t have enough examples, which makes it difficult to decide how to even begin some problems.4) The book doesn’t do a good job of introducing major sections, i.e. providing the reasons and motivation for the next section. Hamilton is much better in this regard.You’re probably stuck with this book because, like me, it is required for a course. It’s apparently the gold standard. Another source may or may not help. For example, there are different approaches and terminology between this book and Hamilton.

⭐An excellent book in every way! I heartily recommend it for its clear coverage of main topics and its breadth!

⭐This 6th edition has some publication annoyances, not the content. First, script fonts are unreadable with faint letters, and it should not be allowed in this high price book. Second, headers are written as “Introduction to Mathematical Logic” in all even pages of the book, so it’s useless to catch which section I am reading. Third, the “Appendix C” uses logic symbols of the first edition, so it’s inconsistent to the notations given in the main body.

⭐This book certainly has breadth. It’s ok as a reference book, but it’s very poor as an introductory text. The guy who gave it 5 stars obviously knew the material before he read it here. A far better introduction is “A Profile of Mathematical Logic” by the philosopher Howard Delong.

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