Product Description
Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Gödel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Gödel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index.
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Customer Reviews (4)

Still very usefull
There are many books on logic, but this, written by one of the chief logicians of the 20th century, deserves a place on your bookshelf. The informations and the exposition style are solid, clear and still new to many. The author also explains the historical motivations for each new concept he talks about, and this alone should make up your mind about buying this book.
But I have seen more modern approaches, and maybe better ones. It's possible to learn so much from this book, and so much that you'll need no other book, least you'd prefer a contemporary way to talk about those things. I would not adopt it for my classes, but I strongly recommend it to my fellows.

Excellent Excellent Book
This book was written by one of the great American mathematical minds of this century.I've read it cover to cover and it happens to be my favorite logic book for its scope, depth, and clarity.Kleene uses a combined model-theoretic and proof-theoretic approach, and derives many interesting results relating the two (he also gives mention to special axioms for Intuitionistic logic).Although his focus in the first part of the book is on a more or less mathematical treatment of standard first-order predicate logic (augmented later by functions and equality), he also spends considerable time discussing the ways in which formal logic can and should be used to analyze "ordinary language" statements and arguments.After setting the groundwork, he moves onto subjects such as set theory, formal axiomatic theories, turing machines and recursiveness, Godel's incompleteness theorem, Godel's completeness theorem, and just about every interesting subject relating to logic in the first half of the twentieth century.

For the mathematically inclined self-teacher, Kleene's exposition should not be difficult at all, in fact I found it remarkably clear compared to other mathematical treatments of the subject (which are necessary if one wants to understand the deeper results).I suppose less mathematically inclined readers could try Irving Copi's "Symbolic Logic" as a start, although even that requires some mathematical proficiency, and since it doesn't cover many of the things you will want to know about, you'll end up coming back to a book like Kleene's anyway.So to summarize, if you want to learn the hard stuff (from the first half of the twentieth century--which includes just about everything the layman/philosopher wants to know), there is no better or easier way.

Excellent introduction
I have to agree with the more recent reviewer and disagree with the first one.I don't even have college-level maths; in fact, I failed abysmally in my school-leaving maths exams (I think I got an F).I wanted to read this because, now in my mid-30s, I had got very interested in various mathematical topics (game theory, number theory, logic) and was sick of just reading popular scientific books about them that assumed that you didn't know how to read the symbols.I ordered this to get me started on logic.

Kleene does an excellent job of introducing a novice like me to the first principles; it's true that he doesn't hang about, and he has a way of bullying his readers into making the effort to understand by dropping sarcastic little remarks like 'Anyone who cannot follow this is clearly mentally sluggish', years of teaching logic in Madison, WI clearly finding payback right there.Some readers may find that kind of thing overbearing, but I found it bracing.I admit that I'm only on page 14, but already I can find the scope of a propositional connective, and when I woke up this morning I had never heard of such a thing.

I thoroughly recommend this book; a brisk, clear, ruthlessly no-nonsense introduction to the subject.Maybe it's not 'Mathematical Logic for Dummies', but Kleene would probably crack that dummies shouldn't be attempting the subject in the first place.

Not for the autodidact
Ten years ago, I took an undergraduate course in symbolic logic.Wishing recently to refresh my (extremely rusty) memories of the propositional calculus and the first-order predicate calculus, I picked up this meaty text and was extremely dismayed to find myself soundly defeated within the first few pages.Kleene does not even make a pretense of holding the reader's hand:either you get it or you don't.There is nothing even remotely "user-friendly" about this book's presentation of its material.

If one were to read this book under the guidance of a teacher, I think it might be worthwhile.It may not be fair for me to blame the author for my inability to understand his writing.If you're smarter than I am, you might breeze right through it.

I cannot recommend this book, though, good though it may be, for anyone who wishes to teach him/herself logic, nor for anyone who wishes to brush up on the subject.There are exercises for the reader to test his/her understanding of the material, but no answer key is provided.This is heavy-duty stuff, and not well-suited to the self-teacher. ... Read more

Customer Reviews (3)

Five stars for content, three and a half stars for the new edition
Kleene's textbook is one of the fundamental texts of mathematical logic. It is easy to see why it is (supposedly) the most cited book in the mathematical logic literature. It is a model of clear explanation, and it does a better job of motivating the subject than any other textbook I have read (I mean deep intellectual and historical motivation of the subject, not the kind of motivation found in introductory logic books about what deduction is, and why learning logic is a good thing to do). Ishi press are to be thanked for making it readily available again at a low price. This edition however is a little on the cheaply made side; this edition was scanned from an older edition, and there are faint copy lines on most pages, so it looks like a photocopy. The pages are glued to the spine, and the binding is not flexible and does not appear all that durable. This means this edition is probably not ideal for serious study as the book will not lay out flat, and forcing it to do so may crack the spine. Nevertheless, if you are interested in mathematical logic this is a must read, and this edition makes it much easier to do so.

The classic of the classics
This is one of those books that don't get old; although it was first published in 1952, and since then much has been made in Mathematical Logic, Kleene's book has that rare position of a book that influenced the subject on its own (and all the teaching books that came after). And if you are willing to understand Mathematical Logic, and principally the reasons behind most of the definitions, I think that this is the best book to start. As a reference it is perhaps the most cited book in the area. But the reading is pleasant, elegant and well motivated. This book has another kind of appeal, in my opinion - research in Logic split after the 1950's in two distinct areas: one, more mathematical in character, is called Model Theory and is strongly abstract, working mainly with the semantics; another, more philosophical and applied, deals mainly with the sintax - this last is the line of research of non-classical logics (philosophically interesting) and of automated procedures, like Smullyan's semantic tableaux for proof-theory (very useful for computation theory). Today the interconnections on these areas, that were initially very close, are dangerously disappearing. Kleene's book, having been written before this separation, is much more comprehensive than the modern textbooks. About the contents: it begins with a (very well) introduction explaining the meaning of Metamathematics. Then it treats Propositional, Predicate Calculi and Formal Number Theory, written in the classical spirit that unfortunately lacks today. The third part deals with recursive functions, and the author was a first-hand researcher in the field, with many important contributions. Finally, the last part treats Model Theory as it was known then (this section can be considered pretty incomplete today).

Enlightening reading
Mathematicians are always aware of the precision and consistency of their asserts, so they need to be trained in the very fundamentals of their science.

This book provides an enlightening vision about the basis ofmathematics exploring such abstract topics as the paradoxes of set theory,transfinite numbers, and much more.

I used this book as a reference in acourse I gave on mathematical logic, set theory, and the fundamentals ofthe number systems. ... Read more

Product Description
Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computation theory, as well as for the strong individuality of his writings on the philosophy of mathematics. Less well-known is his discovery of unusual cosmological models for Einstein's equations, permitting "time-travel" into the past.
This second volume of a comprehensive edition of Gödel's works collects together all his publications from 1938 to 1974. Together with Volume I (Publications 1929-1936), it makes available for the first time in a single source all of his previously published work. Continuing the format established in the earlier volume, the present text includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, a facing English translation of the one German original, and a complete bibliography. Succeeding volumes are to contain unpublished manuscripts, lectures, correspondence, and extracts from the notebooks.
Collected Works is designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science. These volumes will also interest scientists and all others who wish to be acquainted with one of the great minds of the twentieth century. ... Read more

Customer Reviews (1)

Excellent material that fits lots of class uses
A summary of his statement on p. 125 on "Russell's Mathematical Logic" describes the "vicious circle principle: forbids a certain kind of circularity which is made responsible for the paradoxes. The fallacy in these, so it is contended, consists in the circumstance that one defines (or tacitly assumes) totalities, whose existence would entail the existence of certain new elements of the same totality, namely elements definable only in terms of the whole totality." This led to the formulation of a principle which says that "no totality can contain members definable only in terms of this totality, or members involving or presupposing this totality." (The vicious circle principle). (Also a "not applying to itself principle to keep the vicious circle principle from applying to itself p. 126

In describing Russell's theory of types he says, "The paradoxes are avoided by the theory of simple types which is combined with the theory of simple orders - a "ramified hierarchy""

Godel argues that the vicious circle principle is false rather than that classical mathematics is false.

p. 202 "A remark about the relationship between relativity theory and idealistic philosophy (1949a) (Note that this view supports my usual presentations in class on this!)

"The argument runs as follows:Change becomes possible only through the lapse of time. The existence of an objective lapse of time 4, however, means (or, at least, is equivalent to the fact) that reality consists of an infinity of layers of "now"

p. 203 which come into existence successively. But, if simultaneity is something relative in the sense just explained, reality cannot be split up into such layers in an objectively determined way. Each observer has his own set of "nows", and none of these various systems of layers can claim the prerogative of representing the objective lapse of time. 5" ... Read more

Product Description
This digital document, covering the life and work of Stephen Cole Kleene, is an entry from Contemporary Authors, a reference volume published by Thompson Gale. The length of the entry is 578 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

• Place and date of birth and death (if deceased)
• Family members
• Education
• Professional associations and honors
• Employment
• Writings, including books and periodicals
• A description of the author's work
• References to further readings about the author

Product Description
Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century, noted for Gödel's theorem, a hallmark of modern mathematics.The Collected Works will include both published and unpublished writings, in three or more volumes.The first two volumes will consist essentially of Gödel's published works (both in the original and translation), and the third volume will feature unpublished articles, lectures, and selections from his lecture courses, correspondence, and scientific notebooks.All volumes will contain extensive introductory notes to the work as a whole and to individual articles and other material, commenting upon their contents and placing them within a historical framework.This long-awaited project is of great significance to logicians, mathematicians, philosophers and historians. ... Read more

Customer Reviews (1)

The Horror!
I thought I should post a brief note to prevent other potential buyers from being misled by the editorial reviews the way I was._Choice_ says that the editors "deserve the highest praise for the design of the edition."_Mind_ says it is "beautifully produced"._The Journal of Symbolic Logic_ calls it "beautifully prepared"._Zentralblatt_ says that it "was published in a very nice and careful way".

It is reasonable to interpret these statements as referring, at least in part, to the physical appearance of the book; under that interpretation, it is my opinion that these statements couldn't be more wrong.It looks like the volume was printed in the cheapest way possible, and the page layout is amateurish at best.

It is a pity that Oxford University Press hasn't seen fit to publish an edition whose physical beauty is commensurate with the beauty of Godel's ideas. ... Read more

Product Description
Chapters: Stephen Cole Kleene, Eugene Wigner, Harrison Schmitt, Stanislaw Ulam, Henry Barnard, Harry Harlow, Harvey Littleton, James W. Cannon, Paul Ziff, Paul M. Herzog, Selig Perlman, Wallace Stegner, Miloš Velimirović, Lionel Trilling, Warrington Colescott, Robert W. Mcchesney, George Mosse, Denice Denton, Henry Charles Taylor, Oliver Smithies, John Hasbrouck Van Vleck, William Sethares, Harold Cook, Léon Brillouin, Joshua Lederberg, Thomas D. Brock, William Appleman Williams, Susan Pharr, Laura Schwendinger, William Shainline Middleton, Nellie Y. Mckay, William Bleckwenn, Robert J. Havighurst, Alfred W. Mccoy, Mary Lee Hu, Donna Shalala, John R. Commons, David Bordwell, C. Cameron Macauley, Stephen Moulton Babcock, Conrad Elvehjem, Harvey Goldberg, Meredith Gardner, Hans Reese, Elmer Kraemer, Warren Weaver, Keewaydinoquay Peschel, George E. P. Box, Carl R. de Boor, Lorrie Moore, Thomas Chrowder Chamberlin, Ann Althouse, George David Birkhoff, Antony Stretton, Carolyn Martin, Richard T. Ely, Charles F. Manski, Ada Deer, Jesse Lee Kercheval, Samuel A. Stouffer, Doris Dungey, Margaret H'doubler, Jonathan Mark Kenoyer, Ivan Soll, Geoffrey D. Borman, Catherine D. Deangelis, William Lorenz, Richard Davis, Anoop Chandola, James Henry Taylor, Daryl B. Lund, Richard Davidson, John W. Dower, Edgar Buckingham, Allyn Abbott Young, Arthur B. Chapman, Howard Newby, James Danky, John Fiske, Julius Adler, Mitchell J. Nathan, Lewis Leavitt, Dominic W. Massaro, Farrington Daniels, Jim Propp, Arthur Pardee, Albert H. Taylor, Clark L. Hull, Morton Ann Gernsbacher, James Thomson, John D. Wiley, Charles R. Van Hise, Arthur Peabody, Einar Haugen, Thomas J. Scheff, Arne Skaug, James C. Hickman, Teresa de Lauretis, Balthasar H. Meyer, John W. Ryan, William L. Van Deburg, Ryan G. Van Cleave, James R. Lewis, Lawrence Shapiro, Oswaldo Frota-Pessoa, Howard Martin Temin, Archibald Campbell Jordan, Ernest J. Briskey, Martha Fineman, Joseph Jastrow, Ed...More: http://booksllc.net/?id=839100 ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Algèbre de Kleene, Fonction Récursive, Théorème de Récursion de Kleene, Fermeture de Kleene, Théorème D'itération, Théorème Du Point Fixe de Kleene, Théorème de Kleene. Non illustré. Mises à jour gratuites en ligne. Extrait : En mathématiques, une algèbre de Kleene (du nom du logicien américain Stephen Cole Kleene) correspond à l'un des deux concepts suivants : De nombreuses définitions non équivalentes des algèbres de Kleene et des structures liées ont été données dans la littérature. Nous donnerons ici la définition qui semble la plus communément admise aujourd'hui. Une algèbre de Kleene est un ensemble doté des deux lois de composition interne + : A × A → A et · : A × A → A et de l'opérateur * : A → A. Ces lois et cet opérateur sont notés a + b, ab et a* respectivement. Ces opérations satisfont les axiomes suivants : Les axiomes ci-dessus définissent un semi-anneau. On ajoute de plus : Il est dès lors possible de définir un préordre ≤ sur A en postulant a ≤ b si et seulement si a + b = b (ou de manière équivalente, a ≤ b si et seulement il existe c dans A tel que a + c = b). Cette relation d'ordre permet de poser les deux derniers axiomes sur l'opérateur * : De manière intuitive, on peut penser à a + b comme l'union ou le plus petit majorant de a et b, et à ab comme une multiplication croissante, dans le sens où a ≤ b implique ax ≤ bx. L'idée sousjacente à l'opérateur « étoile » est que a*=1 + a + aa + aaa + ... Du point de vue de la théorie de la programmation, on peut interpréter + comme un opérateur de « choix » non déterministe, · comme la « composition séquentielle » et * comme l'« itération ». Soient Σ un ensemble fini (un « alphabet ») et A l'ensemble des expressions rationnelles sur Σ. Deux expressions rati...http://booksllc.net/?l=fr ... Read more

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Chapters: Intuitionism, Stephen Cole Kleene, Intuitionistic Logic, Luitzen Egbertus Jan Brouwer, Brouwer-hilbert Controversy, Michael Dummett, Intuitionistic Type Theory, Constructive Set Theory, Constructive Analysis, Arend Heyting, Heyting Arithmetic. Source: Wikipedia. Pages: 71. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In a foundational controversy in twentieth century mathematics, L. E. J. Brouwer, a supporter of intuitionism, opposed David Hilbert, the founder of formalism. The background for the controversy was set with David Hilbert's axiomatization of geometry in the late 1890s. In his biography of Kurt Gödel, John W. Dawson, Jr summarizes the result as follows: "At issue in the sometimes bitter disputes was the relation of mathematics to logic, as well as fundamental questions of methodology, such as how quantifiers were to be construed, to what extent, if at all, nonconstructive methods were justified, and whether there were important connections to be made between syntactic and semantic notions." (Dawson 1997:48)Dawson observes that "partisans of three principal philosophical positions took part in the debate" (ibid) the logicists (Gottlob Frege and Bertrand Russell), the formalists (David Hilbert and his "school" of collaborators), and the constructivists (Henri Poincaré and Hermann Weyl); within this constructivist school was the radical self-named "intuitionist" L.E.J. Brouwer. The following sections will expand these disputes noted by Dawson. Brouwer in effect founded the mathematical philosophy of intuitionism as a challenge to the then-prevailing formalism of David Hilbert and his collaborators Paul Bernays, Wilhelm Ackermann, John von Neumann and others (cf. Kleene (1952), p. 4659). As a variety of constructive mathematics, intuitionism is essentially a philosop...More: http://booksllc.net/?id=19245793 ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Donald Knuth, Jonathan Bowen, Stephen Cole Kleene, Joseph Sifakis, Robert Floyd, Patrick Cousot, Amir Pnueli, Charles Antony Richard Hoare, Thomas Henzinger, Jean-Raymond Abrial, Jeannette Wing. Non illustré. Mises à jour gratuites en ligne. Extrait : Donald Ervin Knuth () (10 janvier 1938 à Milwaukee, Wisconsin, États-Unis) est un informaticien américain de renom et professeur émérite en informatique à l'université Stanford (États-Unis) (en tant que « Professeur émérite de l'art de programmer »). Il est un des pionniers de l'algorithmique et a fait de nombreuses contributions dans plusieurs branches de l'informatique théorique. Il est l'auteur d'une centaine d'articles et d'une dizaine de livres sur l'algorithmique et les mathématiques discrètes ; les 3 premiers volumes de The Art of Computer Programming (TAOCP) demeurent des ouvrages de référence, ce qui est exceptionnel dans une science comme l'informatique, qui évolue très rapidement. Afin d'avoir une bonne qualité de mise en page pour la deuxième édition de son TAOCP, Knuth a créé deux logiciels libres, par la suite largement utilisés en typographie professionnelle et en mathématiques, TeX et Metafont. Son intérêt pour la typographie l'a également poussé à créer la police Computer Modern, police par défaut de TeX. Né à Milwaukee, dans le Wisconsin, Knuth a reçu son bachelor's degree summa cum laude et son master's degree (les deux simultanément, le jury considérant son travail de B.Sc. comme valant un M.Sc.) en mathématiques en 1960 du Case Institute of Technology (devenu depuis université Case Western Reserve). Sa première analyse d'algorithme remonte à l'été 1962. Knuth découvre à cette occasion un lien entre l'efficacité d'un algorithme de hachage et des mathéma...http://booksllc.net/?l=fr ... Read more

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Chapters: Katharine Hepburn, Stephen Cole Kleene, Barbara Mcclintock, Frederick Law Olmsted, Jeannine Taylor, Wallace Stevens, Harriet Beecher Stowe, Marcus Camby, Henry Barnard, J. P. Morgan, William Gillette, L. Paul Bremer, Bill O'reilly, Stephenie Meyer, Elizabeth May, Stephanie Mcmahon, David Hayes, Wilford Woodruff, John G. Rowland, George Tuska, Samuel Colt, Charles Nelson Reilly, Dore Gold, Thomas Welles, Thomas Hooker, Edward Ralph May, Sophie Tucker, Brooke Burke, John Carney, Donald Baechler, Sol Lewitt, Parker Pennington, Troy Duffy, Eric Mangini, Richard Muenz, Bull Curry, Doug Hoffman, Mason Welch Gross, Martha Bulloch Roosevelt, Will Friedle, Bill Rodgers, Tom Tryon, Jackie Mclean, Jay Mcinerney, Herbert J. Sweet, Ben Cooper, Arthur Everett Austin, Jr., Frank Fasi, Jeff Porcaro, Thomas Hopkins Gallaudet, Marilyn Borden, Jenna Dewan, Moe Drabowsky, Robert O. Tyler, Robert Epstein, Justin Smith, Robert E. Dolan, John Levitow, Will Solomon, Louis Nye, Linda Evans, Johann Smith, Jacob Komar, Gary Merrill, Jack Elliott, Susy Clemens, Jared Jordan, Anna Sokolow, Henry J. Mansell, Harold J. Berman, Fred Curry, Mark Mcgrath, Frank Eaton, Eugene Robinson, Dwight Freeney, Henry Pitkin, Niles Welch, John Milton Niles, Colin Mcenroe, William Wadsworth, Craig Janney, Emma Tillman, John Webster, Rosalyn Borden, Maggie Cassella, John Fiske, Richard Donchian, August Coppola, Phil Tonken, Merrick Alpert, Rick Mahorn, Edward Gaffney, Eileen Albrizio, Dwight William Tryon, William E. Dodge, Irving Wiltsie, Mark Longwell, Robert W. Riscassi, Edward Bennett Williams, John Gregory Dunne, Mike Kellin, Thomas H. Seymour, Chris Landreth, Clarence Barbour, William O'neill, Bruce Hyer, Totie Fields, Eriq La Salle, Simon Prescott, Sabrina Tavernise, Thomas Ian Griffith, Constance Carrier, Emil Richards, James Dixon, Jeremiah Wadsworth, David Tyler, Joza Karas, Alison Hawthorne Deming, Barbara Kolb, Jamaal Branch, Cindy Rogers, Seth P. Wa...More: http://booksllc.net/?id=314924 ... Read more

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Introduction to mathematics. ... Read more