Gödel's incompleteness theorem - recommended reading

This page lists books and other material related to my Gödel's incompleteness theorem project

Websites

Information about Kurt Gödel

The Kurt Gödel Society website has information about Gödel as well as organising conferences on mathematical logic.

SimplyGödel is a new site with interviews with authors who have written about Gödel and his work.

Formalized proofs

Freek Wiedijk has a list of formalizations of significant theorems

Russell O’Connor describes his constructive proof of the Gödel's theorem using the Coq proof assistant.

The Hilbert II links page has plenty more links to relevant sites.


General Books

forever Undecided Raymond SmullyanOxford University Press, 1987ISBN: 0192801414
cover This book gives a gentle introduction to the deep results of Gödel's incompleteness theorems via a series of puzzles for the reader to ponder.
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Mathematical Fallacies and Paradoxes
Bryan Bunch
Dover Publications, 1982ISBN: 0486296644
cover In this book Brian Bunch describes some of the unexpected results of mathematics, including reasons why you might need to watch your step. The book includes a look at self reference and the paradoxes of set theory, leading up to a well written explanation of Gödel's incompleteness theorem.
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Godel, Escher, Bach Douglas HofstadterPenguin, 1979ISBN: 0140289208
cover Hofstadter's classic work, looking at a wide range of topics concerning the mind, patterns and self-reference, and of course Gödel's incompleteness theorem.
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I am a strange loop Douglas HofstadterBasic books, 2007ISBN: 0465030785
cover In this book Hofstadter expands on one of the ideas of his earlier work, the parallelism between Gödel's incompleteness theorem and the emergence of mind and the self. In looks at Gödel's theorem from several different angles, providing a number of intruiging analogies of its strange type of mixing of levels.
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Godel's proof
Ernest Nagel and James R Newman
Routledge, 1958ISBN: 0415355281
cover This book gives a clear explanation of the basics of the proof of Gödel's incompleteness theorem. It would be useful for those wishing to get a clear idea of Gödel's theorem without getting too technical, and to go further than what is given in most popular treatments of the subject
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Godel's theorem : an incomplete guide to its use and abuse
Torkel Franzen
Peters, 2005ISBN: 1568812388
cover One of my reasons for working on this project was to show that Gödel's theorem isn't about some mysterious notion of self reference, but leads to a definite statement which is unprovable from a given set of axioms. In this book Torkel Franzen examines various ways that this theorem has been wrongly quoted, and tries to set the reader straight on what it is really about. He looks at what has been said about incompleteness in physics, in theology and of course in various postmodern ramblings. It would be useful for those readers who want to go beyond the usual popular accounts and get Gödel's theorem clear in their minds.
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Meta Math!:The Quest for Omega Gregory ChaitinAtlantic Books, 2005ISBN: 1843545241
cover Gregory Chaitin is also trying to remove some of the mystery of Gödel's incompleteness theorem, showing that it is part of a more general principle of how computability is limited by complexity (rather than being based on mysterious ideas of self-reference). In this book he gives an account of some of his work.
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Biographies of Gödel

Logical dilemmas John W DawsonPeters, 1997ISBN: 1568810253
cover John W Dawson has sifted through the massive amounts of paperwork that Gödel left, to produce this detailed but readable account of Gödel's life.
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A madman dreams of Turing machines
Janna Levin
Oxford University Press, 2008ISBN: 978029764546
cover Gödel and Turing never met, but one can speculate what would have happened if they did. This book has plenty of biographical information on these two geniuses in a fictional account of their interactions.
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Textbooks

The Foundations of Mathematics
Ian Stewart and David Tall
Oxford University Press, 1977ISBN: 0198531656
cover If you want to understand whats going on with my applets or any other proof of Gödel's theorem, you will need some knowledge of axioms and the structure of number systems. This book gives an excellent introduction to these subjects.
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Metamathematics, machines, and Godel's proof
N Shankar
Cambridge University Press, 1994ISBN: 052142027X
cover There have been other computer based proofs of Gödel's incompleteness theorem, although none have actually produced the undecidable sentence for the reader - rather their purpose is the extra rigor that a computer based proof can provide. This book describes the construction of such a proof, based on the LISP programming language
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Introduction to mathematical logic
Elliot Mendelson
Chapman and Hall, 1997ISBN: 0412808307
cover This is not the simplest way of approaching Gödel's theorems - it goes into a lot of detail of quantification theory before getting on to its application to arithmetics. But in chapter 3 it does actually use the axioms of arithmetic to derive a number of proofs, and for that reason alone it's worth taking a look at.
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Computability and logic
George S Boolos ,John P Burgess and Richard C Jeffrey
Cambridge University Press, 2002ISBN: 0521809754
cover This book is aimed at those wishing to study mathematical logic at the undergraduate level. It starts with a gentle introduction to the subject, but also includes some of the more advanced topics.
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Gödel's's incompleteness theorems Raymond SmullyanOxford University Press, 1992ISBN: 0195046722
cover This isn't the easiest introduction to Gödel's work, but it sticks to the point rather than trying to deal with the whole of mathematical logic, and so provides a comprehensive treatment of Gödel's and related theorems in a concise book
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Incompleteness in the land of sets
Melvin Fitting
College Publications, 2007ISBN: 1904987346
cover A straightforward look at Gödel's incompleteness theorems, using various links between the integers and structures built out of sets.
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On formally undecidable propositions of Principia mathematica and related systems
Kurt Gödel
Dover Publications, 1931ISBN: 0486669807
cover This is a reprint of one of the most significant of all mathematical papers - Gödel's proof of his incompleteness theorem.
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