Elliot Mendelson

Introduction to mathematical logic

My main reason for recommending Elliot Mendelson's Introduction to mathematical logic to someone wishing to study mathematical logic is the start of the third chapter (of 5). This chapter is on formal number theory, and starts off with a list of axioms and then some proofs. That's what mathematical logic is all about isn't it? Well maybe it's more about metaproofs - that is proofs about what you can prove, and certainly that is the main content of this book. However, I feel that having a few pages of the proofs you are dealing with is vital to give the student a foothold in this difficult subject, but, somewhat surprisingly, its difficult to find such proofs in books at this level.

The first chapter is on the (relatively simple) propositional calculus. The second deals with quantification theory - I would recommend that you look at the start of chapter 3 to start with, so as to have a concrete example. The later parts of chapter 3 get on to more complicated mathematical logic, such as Gödel's incompleteness theorem. Chapter 4 is on set theory. Now you may have come across set theory at school, but I have to tell you that the axiomatic version is a totally different ball game. But with the introduction to axiomatics from the previous chapters, this book would be a good place to start studying it. The fifth chapter is on computability. I wouldn't suggest this book as a starting point for this - it's much easier to approach it via real computers. However, it could be useful for seeing the links with other forms of logic.

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Hardcover 440 pages  
ISBN: 0412808307
Salesrank: 2578018
Published: 1997 Springer
Marketplace:New from $72.66:Used from $40.02
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Hardcover 440 pages  
ISBN: 0412808307
Salesrank: 3872250
Weight:1.68 lbs
Published: 1997 Chapman and Hall/CRC
Marketplace:New from £72.00:Used from £57.00
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Hardcover 440 pages  
ISBN: 0412808307
Salesrank: 4127299
Weight:1.68 lbs
Published: 1997 Springer
Marketplace:New from CDN$ 152.00:Used from CDN$ 79.90
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Product Description
The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them.
Introduction to Mathematical Logic includes:
  • propositional logic
  • first-order logic
  • first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski
  • axiomatic set theory
  • theory of computability
    The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.