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1. Godel's Incompleteness Theorems (Oxford Logic Guides) by Raymond M. Smullyan | |
Hardcover: 160
Pages
(1992-08-20)
list price: US$210.00 -- used & new: US$65.63 (price subject to change: see help) Asin: 0195046722 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
A clear presentation of Godel's proof
Well Worth The Investment
A very good book but requires correction of typos
Finally -- Straight Talk About Incompleteness! The book has much of interest to those who wish to pursue the subject of the incompleteness and/or consistency of mathematics, or to come at Goedel from a number of angles. For me, though, the first 3 chapters were enough. I just wanted to find out how K.G. did what he did. Now I know, and I know where to go if I need even more. The exercises are helpful to keep you on track and test your understanding. They also contribute materially to the exposition. A stumbling-block for many readers will be the extremely abstract nature of the discussion, and the new notations and definitions that constantly come at one. Viewing numbers as strings and strings as numbers (and knowing when to switch from one view to another) will be confusing at first. This is the hard part: what Goedel did, in essence, is demonstrate that one can view proofs in two ways � as numbers, and as strings of characters. As in viewing an optical illusion, it is sometimes tough to hold the proper picture in mind. Smullyan�s book �First-Order Logic� is enough preparation for this work. One must here, even more than there, keep straight the difference between the �proofs� that are part of the subject matter (and so are strings of characters), and the proofs we go through that verify facts about these strings. Before we started reading this book, of course, we had some informal sense that we were going to prove something about proofs. What we are REALLY doing, though, is proving something about �proofs�. You get the picture. Goedel must have been a lot of fun at parties.
Mainline Incompleteness with this Book! This title is a difficult read but the only prerequisite isa familiarity of first-order logic equivalent to a one semester collegecourse. A lot of the proofs are based on new material and are easier tounderstand than the original work by KG. An added benefit is theexercises.They are not impossible and aid in one's understanding. This book is well worth the work in demands. ... Read more |
2. There's Something About Godel: The Complete Guide to the Incompleteness Theorem by Francesco Berto | |
Paperback: 256
Pages
(2009-11-16)
list price: US$27.95 -- used & new: US$20.03 (price subject to change: see help) Asin: 1405197676 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
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Customer Reviews (2)
Enhanced my understanding
A perpetuation of a fundamental falsehood |
3. The Shackles of Conviction: A Novel about Kurt Gödel and his Incompleteness Theorem by James R Meyer | |
Paperback: 364
Pages
(2008-05-01)
list price: US$34.00 -- used & new: US$31.77 (price subject to change: see help) Asin: 190670600X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A COMPLETE MISUNDERSTANDING OF GÖDEL'S THEOREM |
4. Aspects of Incompleteness Lecture Notes in Logic 10 (Lecture Notes in Logic, 10) by Per Lindstrom | |
Paperback: 170
Pages
(2003-11)
list price: US$35.00 -- used & new: US$153.53 (price subject to change: see help) Asin: 156881173X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Solid Introduction to Logic |
5. Aspects of Incompleteness (Lecture Notes in Logic) by Per Lindstroem | |
Paperback: 132
Pages
(1997-01-15)
list price: US$42.00 Isbn: 3540632131 Canada | United Kingdom | Germany | France | Japan | |
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6. Proof Theory: Gödel's Incompleteness Theorems | |
Paperback: 344
Pages
(2010-09-15)
list price: US$41.76 -- used & new: US$41.76 (price subject to change: see help) Asin: 1156574587 Canada | United Kingdom | Germany | France | Japan | |
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7. The Incompleteness Phenomenon by Martin Goldstern, Haim Judah | |
Hardcover: 218
Pages
(1995-06-15)
list price: US$54.00 -- used & new: US$54.00 (price subject to change: see help) Asin: 1568810296 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (4)
Corrected second printing exists
Let it go out of print
Nope, didn't like it.
A good simplification for teaching In fact, the main problem with the book is that the assumptions are never made quite clear. The authors say several times that their result is weaker than Goedel's, but never say why. A discussion of this somewhere in the book would be helpful--both to students and profs. Presumably they do not use the full strength of a standard model of the Peano axioms, but it would be a chore to go through and see just what they do use. I taught this book as a one semester course for students who had previously seen predicate logic in an intro course. To fit it into a semester I skipped the chapter on model theory (not needed for the incompleteness theorem) and the material at the end on recursive functions. The book gives a very pretty account of induction, stressing from the start that the natural numbers are just one case of an inductive structure. This made later inductions on, say, well-formed formulas, very clear to the class. The students got the compactness theorem very easily, as they had not in other class I've taught from other books. The short account of non-standard models for arithmetic is helpful in showing that Goedel's theorem is *not* about whether the Peano axioms say all there is to know about arithmetic--the fairly simple compactness theorem already shows no first order theory can do that. I expect to use this book again the next time I teach the subject. ... Read more |
8. Godel's Incompleteness Theorem; Little Mathematics Library by V. A. Uspensky | |
Paperback:
Pages
(1987)
Asin: B000SAITQY Canada | United Kingdom | Germany | France | Japan | |
9. Number Theory and Mathematical Logic: Godel's Incompleteness Theorems by OU Course Team | |
Paperback: 40
Pages
(2004-01-01)
Isbn: 0749257571 Canada | United Kingdom | Germany | France | Japan | |
10. Typographical Number Theory: Axiom, Natural Numbers, Douglas Hofstadter, Gödel, Escher, Bach, Peano Arithmetic, Gödel's Incompleteness Theorems | |
Paperback: 76
Pages
(2010-03-14)
list price: US$47.00 -- used & new: US$41.99 (price subject to change: see help) Asin: 6130537093 Canada | United Kingdom | Germany | France | Japan | |
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11. Metatheorems: Entscheidungsproblem, Gödel's Completeness Theorem, Compactness Theorem, Gödel's Incompleteness Theorems | |
Paperback: 80
Pages
(2010-05-02)
list price: US$19.99 -- used & new: US$19.99 (price subject to change: see help) Asin: 1155221850 Canada | United Kingdom | Germany | France | Japan | |
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12. Godel's Incompleteness Theorems by Open University Course Team | |
Paperback: 40
Pages
(2009-05-16)
-- used & new: US$39.98 (price subject to change: see help) Asin: 0749222743 Canada | United Kingdom | Germany | France | Japan | |
13. Kolmogorov complexity: English language, Complexity, Turing completeness, Godel´s incompleteness theorems, Halting problem, Grammar induction, List of ... in theoretical computer science. | |
Paperback: 88
Pages
(2009-11-24)
list price: US$51.00 -- used & new: US$47.97 (price subject to change: see help) Asin: 6130216874 Canada | United Kingdom | Germany | France | Japan | |
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14. Mathematical Logic: Proofs of Completeness and Incompleteness: An entry from Gale's <i>Science and Its Times</i> by Eric V. D. Luft | |
Digital: 3
Pages
(2000)
list price: US$3.90 -- used & new: US$3.90 (price subject to change: see help) Asin: B0027UWVTY Canada | United Kingdom | Germany | France | Japan | |
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15. Redundancies in the Hilbert-Bernays derivability conditions for Godel's second incompleteness theorem (Research report / Carnegie Institute of Technology. Dept. of Mathematics) by Robert G Jeroslow | |
Unknown Binding:
Pages
(1972)
Asin: B000737N28 Canada | United Kingdom | Germany | France | Japan | |
16. Godel's Incompleteness Theorem (Little Mathematics Library) by V. A. Uspensky | |
Paperback:
Pages
(1989-03)
Isbn: 0828534934 Canada | United Kingdom | Germany | France | Japan | |
17. GÖDEL'S INCOMPLETENESS THEOREMS: An entry from Gale's <i>Encyclopedia of Philosophy</i> by Vann McGee | |
Digital: 13
Pages
(2006)
list price: US$10.90 Asin: B001SCJP1O Canada | United Kingdom | Germany | France | Japan | |
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18. GÖDEL's INCOMPLETENESS THEOREM: An entry from Macmillan Reference USA's <i>Encyclopedia of Science and Religion</i> by W. M. PRIESTLEY | |
Digital: 2
Pages
(2003)
list price: US$1.90 Asin: B001TZKAR8 Canada | United Kingdom | Germany | France | Japan | |
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19. GoÌˆdel's incompleteness theorem (Little mathematics library) by V. A UspenskiiÌ† | |
Unknown Binding:
Pages
(1987)
Asin: B0007BL57O Canada | United Kingdom | Germany | France | Japan | |
20. The incompleteness theorems (Communications of the Mathematical Institute, Rijksuniversiteit Utrecht ; 4) by H. P Barendregt | |
Unknown Binding: 59
Pages
(1976)
Asin: B0006E3RUK Canada | United Kingdom | Germany | France | Japan | |
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