Introduction to Mathematical Logic, 4th edition / Edition 4by Elliott Mendelson, Mendelson Mendelson
Pub. Date: 06/01/1997
Publisher: Taylor & Francis
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… See more details below
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.
Table of ContentsIntroduction
The propositional calculus
Formal number theory
Axiomatic set theory
Answers to selected exercises
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Most Helpful Customer Reviews
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This is no introduction; while it begins with the beginning, many theorems and proofs require a lot of mathematical maturity. Many exercises would be difficult for professionals in the field. The propositional calculus axioms are nicer than the usual ones. But Mendelson gets bogged down in difficult creative proofs. This is a waste of effort, because there exist decision procedures for propositional logic (eg, Quine's truth value analysis). Fairly good intro to model theory. The treatment of set theory nicely deviates from the ZF orthodoxy, favouring NGB and presenting other viewpoints as well. Covers a lot of material, with many references. Almost nothing said about the category theory perspective on logic and set theory. The upper case script font used for some concepts can be hard to read.