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  3. Computability and Logic
  • Cited by 128
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2002
Online ISBN:
9781139164931
DOI:
https://doi.org/10.1017/CBO9781139164931
Subjects:
Computer Science, Logic, Philosophy, Computing: General Interest
Information

Book description

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.

Reviews

‘… gives an excellent coverage of the fundamental theoretical results about logic involving computability, undecidability, axiomatization, definability, incompleteness, etc.’

Source: American Math Monthly

‘The writing style is excellent: although many explanations are formal, they are perfectly clear. Modern, elegant proofs help the reader understand the classic theorems and keep the book to a reasonable length.’

Source: Computing Reviews

‘… a valuable asset to those who want to enhance their knowledge and strengthen their ideas in the areas of artificial intelligence, philosophy, theory of computing, discrete structures, mathematical logic. It is also useful to teachers for improving their teaching style in these subjects.’

Source: Computer Engineering

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Contents

Page 1 of 2

Contents

Page 1 of 2

References
Annotated Bibliography
Annotated Bibliography
General Reference Works
Barwise, Jon (1977) (ed.), Handbook of Mathematical Logic (Amsterdam: North Holland). A collection of survey articles with references to the further specialist literature, the last article being an exposition of the Paris–Harrington theorem
Gabbay, Dov and Guenthner, Franz (1983) (eds.), Handbook of Philosophical Logic (4 vols.) (Dordrecht: Reidel). A collection of survey articles covering classical logic, modal logic and allied subjects, and the relation of logical theory to natural language
Van Heijenoort, Jean (1967) (ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (Cambridge, Massachusetts: Harvard University Press). A collection of classic papers showing the development of the subject from the origins of truly modern logic through the incompleteness theorems
Textbooks and Monographs
Enderton, Herbert (2001), A Mathematical Introduction to Logic, 2nd ed. (New York: Harcourt/Academic Press). An undergraduate textbook directed especially to students of mathematics and allied fields
Kleene, Steven Cole (1950), Introduction to Metamathematics (Princeton: van Nostrand). The text from which many of the older generation first learned the subject, containing many results still not readily found elsewhere
Shoenfield, Joseph R. (1967), Mathematical Logic (Reading, Massachusetts: Addison-Wesley). The standard graduate-level text in the field
Tarski, Alfred, Mostowski, Andrzej, and Robinson, Raphael (1953), Undecidable Theories (Amsterdam: North Holland). A treatment putting the Gödel first incompleteness theorem in its most general formulation
By the Authors
Boolos, George S. (1993), The Logic of Provability (Cambridge: Cambridge University Press). A detailed account of work the modal approach to provability and unprovability introduced in the last chapter of this book
Jeffrey, Richard C. (1991), Formal Logic: Its Scope and Limits, 3rd ed. (New York: McGraw-Hill). An introductory textbook, supplying more than enough background for this book

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