Godel's Incompleteness Theorems
Title | Godel's Incompleteness Theorems PDF eBook |
Author | Raymond M. Smullyan |
Publisher | Oxford University Press |
Total Pages | 156 |
Release | 1992-08-20 |
Genre | Mathematics |
ISBN | 0195364376 |
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
An Introduction to Gödel's Theorems
Title | An Introduction to Gödel's Theorems PDF eBook |
Author | Peter Smith |
Publisher | Cambridge University Press |
Total Pages | 376 |
Release | 2007-07-26 |
Genre | Mathematics |
ISBN | 0521857848 |
Peter Smith examines Gödel's Theorems, how they were established and why they matter.
Incompleteness
Title | Incompleteness PDF eBook |
Author | Rebecca Goldstein |
Publisher | W. W. Norton & Company |
Total Pages | 299 |
Release | 2006-01-31 |
Genre | Biography & Autobiography |
ISBN | 0393327604 |
"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.
Godel's Theorem in Focus
Title | Godel's Theorem in Focus PDF eBook |
Author | S.G. Shanker |
Publisher | Taylor & Francis |
Total Pages | 271 |
Release | 2012-08-21 |
Genre | Philosophy |
ISBN | 1134947984 |
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Godel's Proof
Title | Godel's Proof PDF eBook |
Author | Ernest Nagel |
Publisher | Routledge |
Total Pages | 109 |
Release | 2012-11-12 |
Genre | Philosophy |
ISBN | 1134953992 |
The first book to present a readable explanation of Godel's theorem to both scholars and non-specialists, this is a gripping combination of science and accessibility, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Gödel's Theorems and Zermelo's Axioms
Title | Gödel's Theorems and Zermelo's Axioms PDF eBook |
Author | Lorenz Halbeisen |
Publisher | Springer Nature |
Total Pages | 236 |
Release | 2020-10-16 |
Genre | Mathematics |
ISBN | 3030522792 |
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Godel's Theorem Simplified
Title | Godel's Theorem Simplified PDF eBook |
Author | Harry J. Gensler |
Publisher | |
Total Pages | 94 |
Release | 1984 |
Genre | Mathematics |
ISBN |
This helpful volume explains and proves Godel's theorem, which states that arithmetic cannot be reduced to any axiomatic system. Written simply and directly, this book is intended for the student and general reader and presumes no specialized knowledge of mathematics or logic.