Our stores are still open, see our trading hours here
FREE SHIPPING FOR ORDERS OVER $99.
WISHLISTS
Our stores are still open, see our trading hours here

The Introduction to Godel's Theorems

Hardback|Jul 2007
Product Rating: 0

$150.00

Preface, 1. What Gdel's Theorems say; 2. Decidability and enumerability; 3. Axiomatized formal theories; 4. Capturing numerical properties; 5. The truths of arithmetic; 6. Sufficiently strong arithmetics; 7. Interlude: taking stock; 8. Two formalized arithmetics; 9. What Q can prove;...


Special Order Item
0 Available.

Free Shipping
for orders over $99.

You may also like

eBook
An Introduction to Kierkegaard eBook
$16.83
$16.83
in stock
eBook
An Introduction to Philosophy eBook
$62.84
$62.84
in stock
Introduction to Philosophy Paperback
$69.99
$69.99
in stock
eBook
The Spck Introduction to Kierkegaard eBook
$20.65
$20.65
in stock
Philosophy: A Christian Introduction Paperback
$34.99
$34.99
in stock

Preface, 1. What Gdel's Theorems say; 2. Decidability and enumerability; 3. Axiomatized formal theories; 4. Capturing numerical properties; 5. The truths of arithmetic; 6. Sufficiently strong arithmetics; 7. Interlude: taking stock; 8. Two formalized arithmetics; 9. What Q can prove; 10. First-order Peano Arithmetic; 11. Primitive recursive functions; 12. Capturing funtions; 13. Q is p.r. adequate; 14. Interlude: a very little about Principia; 15. The arithmetization of syntax; 16. PA is incomplete; 17. Gdel's First Theorem; 18. Interlude: about the First Theorem; 19. Strengthening the First Theorem; 20. The Diagonalization Lemma; 21. Using the Diagonalization Lemma; 22. Second-order arithmetics; 23. Interlude: incompleteness and Isaacsonas conjecture; 24. Gdel's Second Theorem for PA; 25. The derivability conditions; 26. Deriving the derivability conditions; 27. Reflections; 28. Interlude: about the Second Theorem; 29. Recursive functions; 30. Undecidability and incompleteness; 31. Turing machines; 32. Turing machines and recursiveness; 33. Halting problems; 34. The Church-Turing Thesis; 35. Proving the Thesis? 36. Looking back.
-Publisher

In 1931, the young Kurt G??del published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. G??del also outlined an equally significant Second Incompleteness Theorem.??How are these Theorems established, and why do they matter??? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
-Publisher

PRODUCT DETAIL
  • Catalogue Code 265852
  • Product Code 9780521857840
  • ISBN 0521857848
  • EAN 9780521857840
  • Pages 376
  • Department Academic
  • Category Philosophy
  • Sub-Category General
  • Publisher Cambridge University Uk
  • Publication Date Jul 2007
  • Dimensions 255 x 180 x 26mm
  • Weight 0.405kg

Peter Smith

Peter S Smith is a UK painter and engraver- many of his etchings are found in the book The Way I See It.

Bestsellers in Philosophy

Escape From Reason Paperback
$14.99
$14.99
in stock
Logic Paperback
Logic
Paperback
No rating
$59.99
$59.99
in stock
How Reason Can Lead to God: A Philosopher's Bridge to Faith Paperback
$29.99
$29.99
in stock
A History of Western Philosophy and Theology Hardback
$79.99
$79.99
in stock
How to Read a Book Paperback
$24.99
$24.99
in stock
Australian Author
The Big Picture: Building Blocks of a Christian World View Paperback
$24.99
$24.99
in stock
How to Be Secular (Not) Paperback
How to Be Secular (Not)
Paperback
(1)Rated 5 stars out of 5
$24.99
$24.99
in stock
Hidden Worldviews Paperback
$36.99
$36.99
in stock