Gödel's incompleteness theorem - recommended reading

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

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.

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.

forever Undecided Raymond Smullyan	Oxford University Press, 1987	ISBN: 0192801414
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.

Mathematical Fallacies and Paradoxes Bryan Bunch	Dover Publications, 1982	ISBN: 0486296644
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. Reviews of Mathematical Fallacies and Paradoxes

Godel, Escher, Bach Douglas Hofstadter	Penguin, 1979	ISBN: 0140289208
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. Reviews of Godel, Escher, Bach

I am a strange loop Douglas Hofstadter	Basic books, 2007	ISBN: 0465030785
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. Reviews of I am a strange loop

Godel's proof Ernest Nagel and James R Newman	Routledge, 1958	ISBN: 0415355281
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 Reviews of Godel's proof

Godel's theorem : an incomplete guide to its use and abuse Torkel Franzen	Peters, 2005	ISBN: 1568812388
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. Reviews of Godel's theorem : an incomplete guide to its use and abuse

Meta Math!:The Quest for Omega Gregory Chaitin	Atlantic Books, 2005	ISBN: 1843545241
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. Reviews of Meta Math!:The Quest for Omega

Logical dilemmas John W Dawson	Peters, 1997	ISBN: 1568810253
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. Reviews of Logical dilemmas

A madman dreams of Turing machines Janna Levin	Oxford University Press, 2008	ISBN: 978029764546
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.

The Foundations of Mathematics Ian Stewart and David Tall	Oxford University Press, 1977	ISBN: 0198531656
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. Reviews of The Foundations of Mathematics

Metamathematics, machines, and Godel's proof N Shankar	Cambridge University Press, 1994	ISBN: 052142027X
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 Reviews of Metamathematics, machines, and Godel's proof

Introduction to mathematical logic Elliot Mendelson	Chapman and Hall, 1997	ISBN: 0412808307
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. Reviews of Introduction to mathematical logic

Computability and logic George S Boolos ,John P Burgess and Richard C Jeffrey	Cambridge University Press, 2002	ISBN: 0521809754
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. Reviews of Computability and logic

Gödel's's incompleteness theorems Raymond Smullyan	Oxford University Press, 1992	ISBN: 0195046722
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 Reviews of Gödel's incompleteness theorems

Incompleteness in the land of sets Melvin Fitting	College Publications, 2007	ISBN: 1904987346
A straightforward look at Gödel's incompleteness theorems, using various links between the integers and structures built out of sets. Reviews of Incompleteness in the land of sets

On formally undecidable propositions of Principia mathematica and related systems Kurt Gödel	Dover Publications, 1931	ISBN: 0486669807
This is a reprint of one of the most significant of all mathematical papers - Gödel's proof of his incompleteness theorem.