Intended for logicians and mathematicians, this text is based on Dr. Hamilton's lectures to third and fourth year undergraduates in mathematics at the University of Stirling. With a prerequisite of first year mathematics, the author introduces students and professional mathematicians to the techniques and principal results of mathematical logic. In presenting the subject matter without bias towards particular aspects, applications or developments, it is placed in the context of mathematics. To emphasize the level, the text progresses from informal discussion to the precise description and use of formal mathmematical and logical systems. The revision of this very successful textbook includes new sections on skolemization and the application of well-formed formulae to logic programming; numerous corrections have been made and extra exercises added.
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Most Helpful Customer Reviews
11 of 11 people found the following review helpful:
3.0 out of 5 stars
Fairly good self-study book, but lots of typos,
By "ez_mouse" (Milford, CT United States) - See all my reviews
This review is from: Logic for Mathematicians (Paperback)
I bought this book as a self-study guide for mathemetical logic. It contains a thorough treatment of propositional and predicate calculus, and briefly covers related subjects such as set theory and Goedel's incompleteness theorem. Overall it is fairly good, presenting the topic in a clear concise manner. The low (for a math textbook at least) price and the fact that it contains answers to selected exercises make this a decent choice for a self-study guide. The only problem I had was the fact that this book contains many typographical errors (I have the 1988 revised edition), which can be somewhat confusing in the the early sections of the book and extremely confusing in later chapters, which are difficult enough.
6 of 6 people found the following review helpful:
4.0 out of 5 stars
Excellent in the beginning chapters,
By "ssavage34" (Cambridge, MA United States) - See all my reviews
This review is from: Logic for Mathematicians (Paperback)
"Logic for Mathematicians" starts well, giving clear and formal explanations of formal logical systems and the predicate calculus. There are plenty of examples in the book, many of which clarified difficult or poorly worded definitions. I have been using this book recently to help me understand concepts that are much more tersely introduced in Elliott Mendelson's "Introduction to Mathematical Logic". This latter book may be better for it's later proofs (e.g., Godel's incompleteness theorem), but the early explanations of how the formal systems work is more easily understood from "Logic for Mathematicians". I gave it only four stars, though, because it becomes a bit less readable later on.The proof of Godel's theorem is incomplete; instead, the author uses convincing examples to demonstrate the generality of recursive functions and from there shows Godel's results.
0 of 1 people found the following review helpful:
3.0 out of 5 stars
A fair starter kit,
By Matt Westwood (Reading, UK) - See all my reviews
This review is from: Logic for Mathematicians (Paperback)
This is a fairly useful work for beginners in mathematical logic. However, one gets the idea that Hamilton himself is a bit muddled, as that's how it comes across in places. I wonder whether there is a text on mathematical logic that isn't a bit muddled now I come to think of it.
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Inside This Book
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First Sentence:
Logic, or at least logical mathematics, consists of deduction. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
consistent first order system, disjoint countable sets, recursive partial function, consistent complete extension, least number operator, find statement forms, finitely presented semigroup, same truth function, formal set theory, prenex form, proper axioms, unsolvable word problem, statement calculus, valuation satisfies, predicate letters, valid argument form, tape symbols, deciding membership, first order arithmetic, axiom schemes, statement variables, clausal form, recursive set, consistent extension, first order language Key Phrases - Capitalized Phrases (CAPs): (learn more)
Church's Thesis, Deduction Theorem, Adequacy Theorem, Turing's Thesis, Peano's Postulates, Repeat Exercise New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Logic, or at least logical mathematics, consists of deduction. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
consistent first order system, disjoint countable sets, recursive partial function, consistent complete extension, least number operator, find statement forms, finitely presented semigroup, same truth function, formal set theory, prenex form, proper axioms, unsolvable word problem, statement calculus, valuation satisfies, predicate letters, valid argument form, tape symbols, deciding membership, first order arithmetic, axiom schemes, statement variables, clausal form, recursive set, consistent extension, first order language Key Phrases - Capitalized Phrases (CAPs): (learn more)
Church's Thesis, Deduction Theorem, Adequacy Theorem, Turing's Thesis, Peano's Postulates, Repeat Exercise New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
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31
books
cite this book:
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- Introduction to Mathematical Logic, Fourth Edition by E. Mendelson in Front Matter, and Back Matter
- Set Theory and the Continuum Hypothesis by Paul J. Cohen in Back Matter
- Mathematical Logic by Joseph R. Shoenfield in Back Matter
- Introduction to Metamathematics (Bibliotheca Mathematica) by S.C. Kleene in Back Matter
- Computability and Unsolvability by Martin Davis in Back Matter
See all 11 books this book cites
- Logic by Paul Tomassi on page 150, page 187, and Back Matter
- Logic by Paul Tomassi on page 187, and Back Matter
- Essays in Logic and Ontology (Poznan Studies in the Philosophy of the Sciences and the Humanities 91) (Poznan Studies in the Philosophy of the Sciences & the Humanities) by Jacek Malinowski; Andrzej Pietruszczak (Eds.) on page 168
- How to Prove It: A Structured Approach by Daniel J. Velleman in Back Matter
- Basic Simple Type Theory (Cambridge Tracts in Theoretical Computer Science) by J. Roger Hindley in Back Matter
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