A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.
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Most Helpful Customer Reviews
4 of 4 people found the following review helpful:
4.0 out of 5 stars
Good,
By
This review is from: Notes on Logic and Set Theory (Cambridge Mathematical Textbooks) (Paperback)
The book deals with the elementary parts of logic, computability and set theory from an algebraic and/or "abstract" point of view. Hence it is not really suitable as a first introduction to logic (except possibly for persons of extremely deep insight!) Of course nothing in the book is actually difficult. But the exposition is sketchy and lacks sufficient motivation. Important foundational, motivational, historical side-topics are ignored. The ideas and intuitions shaping the subject are relegated to the background of slick technical developments. As I mentioned below, these really are just notes! Most novices ought to suffer a more traditional exposure to logic first; such as reading [Enderton] or [Ebbinghaus et al.] On the other hand, for people with *some* background and *some* mathematical inclination and *some* sense of mathematical beauty, this book is fun. The abstract approach brings out the essential features of the notions studied in logic, provides slick proofs and makes an implicit case for the unity of mathematics including mathematical logic -- which is the mathematical study of (various aspects of) mathematics itself. I personally like these "abstractions" but if you don't like them or if you don't yet have the necessary background, don't worry: There are other good logic books out there with a lighter touch.
1 of 1 people found the following review helpful:
3.0 out of 5 stars
Good,
By A Customer
This review is from: Notes on Logic and Set Theory (Cambridge Mathematical Textbooks) (Paperback)
The book deals with the elementary parts of logic, computability and set theory from an algebraic and/or "abstract" point of view. Hence it is not really suitable as a first introduction to logic (except possibly for persons of extremely deep insight!) Of course nothing in the book is actually difficult. But the exposition is sketchy and lacks sufficient motivation. Important foundational, motivational, historical side-topics are ignored. The ideas and intuitions shaping the subject are relegated to the background of slick technical developments. As I mentioned below, these really are just notes! Most novices ought to suffer a more traditional exposure to logic first; such as reading [Enderton] or [Ebbinghaus et al.] On the other hand, for people with *some* background and *some* mathematical inclination and *some* sense of mathematical beauty, this book is fun. The abstract approach brings out the essential features of the notions studied in logic, provides slick proofs and makes an implicit case for the unity of mathematics including mathematical logic -- which is the mathematical study of (various aspects of) mathematics itself. I personally like these "abstractions" but if you don't like them or if you don't yet have the necessary background, don't worry: There are other good logic books out there with a lighter touch.
1 of 1 people found the following review helpful:
4.0 out of 5 stars
Appendix to Review Below,
By A Customer
This review is from: Notes on Logic and Set Theory (Cambridge Mathematical Textbooks) (Paperback)
Since my previous review attracted as many "unhelpfuls" as "helpfuls," here is a clarification: If you think my previous review is too terse, don't bother buying this book. Johnstone's exposition is *extremely* terse. The book deals with the elementary parts of logic, computability and set theory from an algebraic and/or "abstract" point of view. Hence it is not really suitable as a first introduction to logic (except possibly for persons of extremely deep insight!) Of course nothing in the book is actually difficult. But the exposition is sketchy and lacks sufficient motivation. Important foundational, motivational, historical side-topics are ignored. The ideas and intuitions shaping the subject are relegated to the background of slick technical developments. As I mentioned below, these really are just notes! Most novices ought to suffer a more traditional exposure to logic first; such as reading [Enderton] or [Ebbinghaus et al.] On the other hand, for people with *some* background and *some* mathematical inclination and *some* sense of mathematical beauty, this book is fun. The abstract approach brings out the essential features of the notions studied in logic, provides slick proofs and makes an implicit case for the unity of mathematics including mathematical logic -- which is the mathematical study of (various aspects of) mathematics itself. I personally like these "abstractions" but if you don't like them or if you don't yet have the necessary background, don't worry: There are other good logic books out there with a lighter touch.
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Inside This Book
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First Sentence:
The function of mathematical logic is to provide formal languages for describing the structures with which mathematicians work, and the methods of proof available to them. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Deduction Theorem, Zorn's Lemma, Prime Ideal Theorem, Compactness Theorem, Church's Thesis, Mostowski's Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The function of mathematical logic is to provide formal languages for describing the structures with which mathematicians work, and the methods of proof available to them. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Deduction Theorem, Zorn's Lemma, Prime Ideal Theorem, Compactness Theorem, Church's Thesis, Mostowski's Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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6
books
cite this book:
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- An Algebraic Introduction to Mathematical Logic (Graduate Texts in Mathematics) by D.W. Barnes in Front Matter
- A Companion to Analysis: A Second First and First Second Course in Analysis (Graduate Studies in Mathematics) by T. W. Korner on page 355
- Categories for Types (Cambridge Mathematical Textbooks) by Roy L. Crole in Back Matter
- Theorem Proving in Higher Order Logics: 11th International Conference, TPHOLs'98, Canberra, Australia, September 27 - October 1, 1998, Proceedings (Lecture Notes in Computer Science) by Jim Grundy on page 170
- Fundamental Structures of Algebra and Discrete Mathematics by Stephan Foldes on page 29
- Foundations of Logic and Mathematics by Yves Nievergelt in Back Matter
See all 6 books citing this book
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