- Paperback: 572 pages
- Publisher: Ishi Press (March 13, 2009)
- Language: English
- ISBN-10: 0923891579
- ISBN-13: 978-0923891572
- Product Dimensions: 6 x 1.3 x 9 inches
- Shipping Weight: 2.1 pounds (View shipping rates and policies)
- Average Customer Review: 4.7 out of 5 stars See all reviews (9 customer reviews)
- Amazon Best Sellers Rank: #968,253 in Books (See Top 100 in Books)
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Introduction to Metamathematics
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Top Customer Reviews
Some criticism it surely deserves: the lack of model theory reveals the book's age (though the reviewer Guilherme thinks this alternative perspective to be a strength). Paul E. Mokrzecki's review rather eccentrically pans the text for using the truth-functional definition of implication (we're all familiar with it: false only when the antecendent is true and the consequent false). Achronymous faults the text for its construction, but so far my copy has beautifully suffered my abuse. Sure, there are a few copy lines, but before this edition I would have had to shell out about two hundred dollars for a copy! I was heartbroken.
And another miracle has occurred: though Chang and Keisler's Model Theory may be a bit dated too (Hodges or Marker are newer, we know we know...), the Dover Publications reprint means that an affordable model theory text can accompany Kleene. The availability of cheap model theory texts makes Kleene's lack of inclusion of this subject far from disastrous.
On the the other hand, "Mathematical Logic" (ML) brings a definite plus, but is by no means a replacement, rather a necessary complement.
As I planned to study both, the problem posed was the order in which one should approach those books : Historically ? By increasing or decreasing difficulty ? In parallel, in order to see how Kleene's ideas -- and the field -- have evolved between 1952 and 1966, and subject by subject ?
I chose the third an most difficult path... And the journey was a thrill !
Here is how I planned this strange exploration : IM, ch. 1 to 7 ; ML, ch. 1 to 4 ; IM, ch. 8 ; IM, Part III ; ML, ch. 5 : IM, ch. 14 ; ML, ch. 6 ; IM, ch. 15.
ML is certainly less difficult but contains a fair amount of footnotes linking it to IM, i.e. studying IM is simply inevitable and enjoyable, even though some parts are really tough and must be "examined in a cursory manner", as suggested by Kleene, e.g. ch. 14 & 15.
IM, part III, is a thorough treatment of recursive functions, the best in my opinion and is not part of ML.
All in all, the two together rank very high in logic books, perhaps highest.
This book now stands in my personal list of key books of Logic, as follows :
1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest
2. D. Goldrei's "Propositional and Predicate calculus"
3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic".
4. P.Read more ›
Most Recent Customer Reviews
The book is a classic one. The rating is about the production. It seems they have produced the book from a copy of the original edition. Read morePublished 19 months ago by Apostolos Syropoulos
I worked in "Foundations" in my thesis(1966) through Wilder. This informed me of intuitionist advances since then. So, it was very helpful.Published on February 25, 2014 by Phillip Couture
One of the greatest contributors to Metamathematics; in particular, tp many-valued logic and its consequences. Very recomendable book, but not for beginners.Published on December 29, 2013 by Juan Valverde
S. Kleene, probably the first giant among the second generation of computation theorists has provided succeeding generations with a compendium of results that would be very hard to... Read morePublished on July 8, 2013 by bruce e litow