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Richard E. Hodel

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An Introduction to Mathematical Logic (Dover Books on Mathematics) Reprint Edition

by Richard E. Hodel (Author)

4.7 46 ratings

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Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy.
An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Gödel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.

ISBN-10

0486497852
ISBN-13

978-0486497853
Edition

Reprint
Publisher

Dover Publications
Publication date

February 20, 2013
Language

English
Dimensions

5.9 x 1.1 x 8.9 inches
Print length

512 pages
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Editorial Reviews

From the Back Cover

Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy.
An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Gödel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.
Dover (2013) republication of the edition published by PWS Publishing Company, Boston, 1995.
See every Dover book in print at
www.doverpublications.com

Product details

Publisher ‏ : ‎ Dover Publications; Reprint edition (February 20, 2013)
Language ‏ : ‎ English
Paperback ‏ : ‎ 512 pages
ISBN-10 ‏ : ‎ 0486497852
ISBN-13 ‏ : ‎ 978-0486497853
Item Weight ‏ : ‎ 2.31 pounds
Dimensions ‏ : ‎ 5.9 x 1.1 x 8.9 inches

Best Sellers Rank: #1,244,791 in Books (See Top 100 in Books)
- #569 in Mathematical Logic
- #2,902 in Mathematics (Books)
- #7,444 in Core

Customer Reviews:
4.7 46 ratings

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John Linstrum

Got What I Needed Out of It

Reviewed in the United States on February 15, 2021

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Honestly, this book gets into the arcana of theories and systems a bit more than I needed, but it still served as a decent semi-introduction/review for a high school math teacher / computer programmer who was trying to help out a former student taking an introductory class in mathematical logic. If you are in a similar situation as I was, I recommend reading the start of each chapter in detail and when it gets too theoretical just skim.

Also, for some reason the first chapter dives pretty hard into advanced concepts like formal systems, relations, decidability, etc. that are arguably more difficult than the bulk of the following chapters. The author recommends to "cover it as needed" in the preface. This is good advice as the next few chapters are a bit easier and more on topic.

Anyway, aside from being rather challenging in parts for a non-expert, it is also extremely well organized and readable with an index etc., hence a reasonable choice even for a less advanced mathematician like myself. If you are looking to touch on more advanced topics (the work of Godel, Tarski, Church, etc.), it will do that too.

2 people found this helpful

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Antti Piironen

The book itself is broad and detailed othervicely with an excellent set of exercises and reviews of the theories from ...

Reviewed in the United States on March 23, 2016

Verified Purchase

Book is well written, except on one parts: now and then the proofs for theorems, lemmas etc. are quite unfinished and as such demand working on them. The book itself is broad and detailed othervicely with an excellent set of exercises and reviews of the theories from basic theories to computability and somewhat decision theory. Indeed, this one can be warmly recommed from beginners to advanged students and hobbyist alike who demand more exercises and good source book to bookstand.

4 people found this helpful

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sam s

Intuitive, Rigorous, Amazing

Reviewed in the United States on October 17, 2018

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This is by far one of the best mathematics books I have read to date. The author clearly has a solid understanding of the material and didn't just copy and paste from previous works in the field.

Highly Recommend if you're interested in mathematics, computer science or philosophy.

3 people found this helpful

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Amazon Customer

Great book, but semi-junk typeface/fonts

Reviewed in the United States on September 5, 2019

Verified Purchase

At first, I didn't really like this book, but it was okay...but I kept studying in...off and on. Meanwhile, I studied many other logic books as well. However, over time, I realized how priceless this book really was. It's quite excellent, especially when you get further in. It also covers lots of material skipped by other books.

6 people found this helpful

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Paulo Argolo

A wonderful book!

Reviewed in the United States on August 12, 2018

Verified Purchase

One of the best books ever written on Logica Matemática!
A must-read!

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Luis Gomez

A nice intro to math logic.

Reviewed in the United States on July 23, 2016

Looks Good.

Strikes an excellent balance between rigor and accessibility

Reviewed in the United States on June 10, 2015

Discovered this book by coincidence, when I was looking online for some details of non-standard models of Peano Arithmetics and Skolem's result on this matter. Almost the entire chaper 6 of the book ("First order theories and Hilbert's Program") is on Google Books, and I found myself rereading other part and proofs as well, simply because of the extreme clarity of developing his arguments.

There are probably more rigorous (introductory) books on mathematical logic - Enderton's "A Mathematical Introduction to Logic" comes to mind, and there are also probably more accessible (but less rigorous) introductions, say Gamut's "Logic, Language, and Meaning, Volume 1", but Hodel's Introduction to Mathematical Logic strikes a very rare balance between the two.

The author is certainly rigorous enough to make this a title on mathematical logic (as opposed to a treatment from the more philosophical side), but he also has a way to cut out some of the more tedious parts for the sake of clarity. I would highly recommend this books for two groups: those who already have a basic introduction to logic and want a maximally accessible, yet thorough introduction to mathematical logic, and those who already read a book like Enderton, but feel they lack some intuitive access to some of the formal results.

A note on the edition: I got the softcover / reprint, and if I could, I would rate the title 5 stars, but the print quality 4, maybe even 3. Low paper quality, narrow margins, all in all, unpleasant. Still, I'm happy to give the title itself 5 stars, but if I could order it again, would probably try to get the hardcover, maybe as a used version to save some money.

6 people found this helpful

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Sam Zimmerman

Great Introductory Logic Textbook

Reviewed in the United States on December 6, 2014

As a philosophy graduate student and mathematics undergraduate, I purchased this textbook looking for a clearer understanding of mathematical logic. I found it exceedingly clear and concise, most importantly there was much clearer than I anticipated development of the key ideas of the text. I particularly enjoyed the section on the Diophantine equations - I had not encountered that idea or material before, and now have a perspicuous view of it. Could not recommend higher for undergraduates with some mathematics background.

11 people found this helpful

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Top reviews from other countries

Amazon Customer

Classic book!!

Reviewed in India on July 10, 2023

Verified Purchase

This dover reprint of original Addison wesley book. It covers everything relevant for CS students. I got new book for 68 INR (40 INR delivery charges). Go for it .

Babaorum

Well written, easy to grasp the ideas with limited effort

Reviewed in France on June 1, 2023

Verified Purchase

The type of writing intended to make the reader's easy. Clear, concise with a limited amount of notations, intuitions are always to the point, this writing allows for a smooth reading of an otherwise difficult topic. Pity editors do force authors to write this way.

Amazon Customer

Clear and concise

Reviewed in Singapore on September 26, 2021

Verified Purchase

Great for self-study.

Xied75

Only done two chapters so far.

Reviewed in the United Kingdom on September 29, 2013

Verified Purchase

Looks like the Dover Books are worth to collect, might buy some more in the serials later. You just can't have enough math.

Goncalo

Great book, even better price

Reviewed in the United Kingdom on May 27, 2019

Verified Purchase

I can't really compare because it's the only book I've read on the topic. I absolutely loved it though and usually textbooks like this are way more expensive.

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