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21. Logic and Structure by Dirk van Dalen, Dirk van Dalen | |
Paperback: 263
Pages
(2008-09-01)
list price: US$54.95 -- used & new: US$36.00 (price subject to change: see help) Asin: 3540208798 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
not for newcomers
Best title ever |
22. Mathematical Logic: Foundations for Information Science (Progress in Computer Science and Applied Logic (PCS)) by Wei Li | |
Hardcover: 273
Pages
(2010-01-22)
list price: US$69.95 -- used & new: US$61.51 (price subject to change: see help) Asin: 3764399767 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines. |
23. A Tour Through Mathematical Logic (Carus Mathematical Monographs) by Robert S. Wolf | |
Paperback: 414
Pages
(2005-01-08)
list price: US$60.95 -- used & new: US$48.75 (price subject to change: see help) Asin: 0883850362 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The word "tour" in the title deserves some explanation. This word is meant to emphasize that this is not a textbook in the strict sense. To be sure, it has many of the features of a textbook, including exercises. But it is less structured, more free-flowing, than a standard text. It also lacks many of the details and proofs that one normally expects in a mathematics text. However, in almost all such cases there are references to more detailed treatments and the omitted proofs. Therefore, this book is actually quite suitable for use as a text at the university level (undergraduate or graduate), provided that the instructor is willing to provide supplementary material from time to time. The most obvious advantage of this omission of detail is that this monograph is able to cover a lot more material than if it were a standard textbook of the same size. This de-emphasis on detail is also intended to help the reader concentrate on the big picture, the essential ideas of the subject, without getting bogged down in minutiae. This book could have been titled "A Survey of Mathematical Logic," but the author’s choice of the word "tour" was deliberate. A survey sounds like a rather dry activity, carried out by technicians with instruments. Tours, on the other hand, are what people take on their vacations. They are intended to be fun. The goal of this book is similar: to provide an introduction to the foundations of mathematics that is substantial and stimulating, and at the same time a pleasure to read. It is designed so that any interested reader with some post-calculus experience in mathematics should be able to read it, enjoy it, and learn from it. Customer Reviews (1)
An in-depth and in-breadth tour of the foundations of mathematics |
24. Mathematical Logic by George Tourlakis | |
Hardcover: 294
Pages
(2008-09-02)
list price: US$105.00 -- used & new: US$79.80 (price subject to change: see help) Asin: 0470280743 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work. Customer Reviews (1)
rigorous introduction |
25. What is Mathematical Logic? by C. J. Ash, J. N. Crossley, C. J. Brickhill, J. C. Stillwell, N. H. Williams | |
Paperback: 96
Pages
(2010-10-18)
list price: US$6.95 -- used & new: US$6.95 (price subject to change: see help) Asin: 0486264041 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
No-nonsense survey of logic
Six Rigorous Lectures - Not for the Faint-Hearted The six chapters are derived from a series of lectures given by the five authors - J. N. Crossley, C. J. Ash, C. J. Brickhill, J. C. Stillwell, and N. H. Williams - at Monash University and University of Melbourne in 1971.The lectures were substantially revised for publication. Only the first chapter, a detailed historical survey of mathematical logic, can be readily appreciated by the non-mathematician. The remaining five chapters examine advanced topics in mathematical logic including the Godel-Henkin Completeness Theorem, Model Theory, Turing machines and recursive functions, Godel's Incompleteness Theorem, and advanced set theory. Chapter 2 introduces the Godel-Henkin Completeness Theorem, a proof that predicate calculus is complete. Chapter 2 is not easy, but it is essential to acquire a reasonable familiarity with predicate calculus before moving forward. Chapter 3 offers a detailed look at model theory, the study of relations between formal languages and the interpretation of formal languages. Topics include Predicate Calculus with Identity, the Compactness Theorem, and the Lowenheim-Skolem Theorems. I had substantial difficulty with the details, but I did gain a general understanding and appreciation for model theory. Chapter 4 addressed in considerable detail a more familiar topic, Turing machines and recursive functions. The discussion concludes with a key proof: there is no algorithm which will enable us to decide, given any particular formula of predicate calculus, whether or not this particular formula is deducible from the axioms of predicate calculus. Chapter 5 was a detailed examination of Godel's Incompleteness Theorem for formal systems that include arithmetic of the natural numbers. I had less difficulty with this topic as I had previously read Godel's Proof by E. Nagel and J. R. Newman. This chapter would very likely be tough going for a reader entirely new to Godel's exceeding complex and abstruse proof. Chapter 6, titled Set Theory, might be better named Advanced Set Theory. I was entirely new to the Axiom of Choice and the Generalized Continuum Hypothesis. I highly recommend this intriguing and lively look at mathematical logic to readers with some familiarity with this rather formidable subject. For readers new to mathematical logic, I suggest that the following books might be better starting points. Foundations and Fundamental Concepts of Mathematics by Howard Eves is outstanding. The chapter titled Logic and Philosophy is an excellent introduction to mathematical logic. The Advent of the Algorithm by David Berlinski is an eclectic, rather bizarre introduction to a complex mathematical topic. Although many reader reviewers aggressively criticize this book, I enjoyed puzzling my way through Berlinski's discursive discussions. Godel's Proof by Ernest Nagel and James R. Newman offers a fascinating look at a mind boggling, incredibly complex, inventive mathematical proof.
Dense but readable Results are clearly and carefully stated; and while sketches of proofs have a hard time staying nontechnical and still meaningful, most such attempts are admirable. A marvel of brevity while not watering anything down. ... Read more |
26. Mathematical Logic (Oxford Texts in Logic) by Ian Chiswell, Wilfrid Hodges | |
Paperback: 296
Pages
(2007-07-12)
list price: US$70.00 -- used & new: US$15.14 (price subject to change: see help) Asin: 0199215626 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
A SUPERLATIVE TEXTBOOK OF LOGIC - one that is without headaches !
Poorly written
Logic: Symbolic & Conceptual |
27. Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions by Eric Schechter | |
Hardcover: 536
Pages
(2005-08-08)
list price: US$92.50 -- used & new: US$59.90 (price subject to change: see help) Asin: 0691122792 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Good to teach or learn logic from |
28. A Course In Mathematical Logic by John Bell, Moshe Machover | |
Hardcover: 600
Pages
(1977-01-15)
list price: US$166.00 -- used & new: US$132.80 (price subject to change: see help) Asin: 0720428440 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (3)
Covers a lot, but not all that well
This is the book you need as a logic primer One day I discovered this book by Bell and Machover. It was exactly what I needed. The first three chapters are just what you need to get a solid grounding in first-order logic, covering the soundness, completeness and compactness theorems. As I was working through the book, I noticed that the incompleteness theorems weren't treated till the 7th chapter -- this, along with the fact that the exercises were so much fun kept me pushing forward one chapter at a time. Chapter 4 deals with Boolean algebras. I'd alreday had quite a bit of general topology before starting this chapter, so when the duality between Boolean algebras and Stone spaces is explored in some detail in the exercises, it was really a blast. A lot of material is covered in this chapter; the authors never tell you that they chose just the material you will need if you go on to study the Boolean algebra approach to forcing. (They actually give you a taste of Boolean-valued models in Chapter 5, but that's it for forcing in this book; however, the first author, Bell, wrote another book called Boolean-Valued Models and Independence Proofs in Set Theory that provides the most complete treatment of the subject available in book form.) Chapter 5 gives a careful treatment of the basics of model theory (which was what I needed). Chapter 6 then gives a very fun treatment of recursion theory. The main material covers enough to prove the equivalence of recursive and computable functions (and computable functions are treated using a special kind of register machine rather than the usual Turing machines). Finally with all the groundwork completed, the authors give a marvelous treatment of the incompleteness theorems, including the usual results about undecidability of Peano arithmetic and the undefinability of truth. The authors go on to develop recursion theory a little further in light of the theorems of Chapter 7 -- enough to solve Post's problem by building two incomparable r.e. degrees. The rest of the book consists of special topics -- intuitionistic logic, set theory, and nonstandard analysis. All this was very good, though I suppose I prefer other treatments of set theory (Kunen or Jech). The strength of this book is that it doesn't gloss over any details -- and this is very important when you first get into mathematical logic. This should be every graduate student's first course on logic!
Probably the most comprehensive Course in Mathematical Logic But, it is surprising to me how difficult it is to find it in any libarary in USA.Even more surprising, however, is that, after all these years, it is notavailable at an affordable price. (It would be hasty to suggest that somepublishers are motivated by greed than a desire to inform and educate, I amsure there are better reasons -- with the reservations that go with sayingthis, of course.). On the cheerful side, I had the good fortune to siton most of this course given by Moshe Machover in London. He is anoutstanding logician and teacher. As a human being he is profound and just.He used to say, with a humorous matter-of-factness, something to the effectthat he hoped we were not filled with "malaise" his favouriteword. The coverage is thorough and deep. The book is sufficientlyadvanced for it to be used as a textbook for a Master Level Introduction inLogic. It wasbeing used in this way at London University (in1979). Thus it takes you further than most logic books that seek to teachthe same set of topics. After covering early theorems in, say, modeltheory, it goes on to prove advanced theorems well beyond the standardtexts on logic. The book, as I mentioned prepares you, relative to theBritish system, for an MA degree -- and so perhaps, a pre-amble to MPhiland, presuemeably,PhD levels. You might need to augment this book withsome other books in Topology, to follow some of the topological theorems). Machover's other logic book, intended for Philosophers is set theory,logic and their limitatins, which locally resembles this book but is on amuch more modest scale and certainly does not cover constructive logic. Hisearliest book was Nonstandard Analysis without tears. In the class, hewould give handouts for proof of some of the exercises. But, if you cannotdo them on your own you should consult some of the bibliographic sources.For instance on Non-standard models you might consult Robinson'sNon-standard Analysis. His coverage of Set Theory, Limitative Results(Goedel results etc.) and Intuitionistic logic is fantastic. Buy it ifyou can afford it. ... Read more |
29. Introduction to Mathematical Logic by Alonzo Church | |
Paperback: 378
Pages
(1996-10-28)
list price: US$67.50 -- used & new: US$42.75 (price subject to change: see help) Asin: 0691029067 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
a classic, but mostly useful as a historical reference
One of the classics In the introduction to the book the author defines the terms and concepts he will use in the book, with a discussion of proper names, constants and variables, functions, and sentences. He adopts the Fregian point of view that sentences are names of a particular kind. His discussion of this is rather vague however, for he does not give enough clarification of the difference between an "assertive" use of a sentence and its "non-assertive" use. Readers will have to do further reading on Frege in order to understand this distinction more clearly, but essentially what Church is saying here is that sentences are names with truth values. The existential and universal quantifiers are introduced as well. And here the author also introduces the concepts of object language and metalanguage, along with a discussion of the axiomatic method. The author distinguishes between informal and formal axiomatic methods. The modern notions of syntax and semantics are given a nice treatment here, and the di scussion is more in-depth than one might get in more modern texts on mathematical logic. Chapter 1 is a detailed overview of propositional logic, being the usual formal system with three symbols, one constant, an infinite number of variables, rules on how to form well-formed formulas, and the rules of inference. The deduction theorem is proved in detail along with a discussion of the decision problem for propositional logic, with the famous truth tables due to W. Quine introduced here. The notions of consistency and completeness are briefly discussed. The discussion of the propositional calculus is continued in the next chapter where a new system of propositional calculus is obtained by dropping the constants from the first one and adding another symbol (negation). The two systems are shown to be equivalent to each other using a particular well-formed formula in the second one to replace the constant in the first. Other systems of propositional calculus are also introduced here, using the idea of primitive connectives such as disjunction, along with various rules of inference. Church also outlines an interesting propositional calculus due to J.G.P.Nicod, which assumes only one primitive connective, one axiom, and only one rule of inference (besides substitution). The author also introduces partial systems of propositional calculus, with the goal of showing just what must be added to these systems to obtain the full propositional calculus. He discusses the highly interesting and thought-provoking intuitionistic propositional calculus, due to A. Heyting, which is a formalization of the famous mathematical intuitionism of L.E.J. Brouwer. The system he discusses is a variant of Heyting's and he gives references to the positive solution of the decision problem for this system. The author ends the chapter with a brief discussion of how to construct a propositional calculus by employing axiom schemata. The author then moves on to what he has termed functional calculi of first order beginning in the next chapter. Called predicate calculi in today's parlance, the author first defines the pure functional calculus of first order, and shows that the theorems of the propositional calculus also follow when considered as part of this system. Free and bound variables are defined, and Church proves explicitly the consistency of this system, and the deduction theorem. The important construction of a prenex normal form of a well-formed formula is discussed, and the author shows that every well-formed formula of the functional calculus is equivalent to some well-formed formula in prenex normal form. In chapter 4, the author gives an alternative formulation of pure functional calculus of first order, wherein rules of substitution are used and axiom schemata are replaced by instances, making the number of axioms finite. The Skolem normal form of a well-formed formula is defined, which sets up a discussion of satisfiability and validity. The author then proves the Godel completeness theorem, which states that every valid well-formed formula is a theorem. This is followed by a very well written discussion of the Skolem-Lowenheim theorem, and an overview of the decision problem in functional (predicate) calculus. In the last chapter of the book the author considers functional (predicate) calculi of second order, which is distinguished from the first order case by allowing the variables to range over what its predicates and subjects represent. In second-order functional calculus, propositional and predicate variables can have bound occurrences. The author discusses the elimination problem and consistency for second-order predicate calculus, and gives a proof of the (Henkin) completeness theorem. A fairly detailed discussion of a logical system for elementary number theory is given, but the treatment involves notation that is somewhat clumsy and the discussion is difficult to follow. ... Read more |
30. Handbook of Mathematical Induction: Theory and Applications (Discrete Mathematics and Its Applications) by David S. Gunderson | |
Hardcover: 921
Pages
(2010-09-14)
list price: US$109.95 -- used & new: US$59.99 (price subject to change: see help) Asin: 1420093649 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn’s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process. Customer Reviews (3)
A "must have" for everyone whose passion lies in the mathematics!
Fantastic resource!
Not a Handbook |
31. Introduction to Mathematical Logic, Third Edition by Elliott Mendelson | |
Hardcover: 341
Pages
(1987-02-28)
list price: US$101.00 -- used & new: US$73.73 (price subject to change: see help) Asin: 0534066240 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (11)
A big mistake
A must have....
twisted pants unleashed on men
Wonderful at the second glance.
Best reference in first step math logic |
32. First Course in Mathematical Logic by Patrick Suppes, Shirley Hill | |
Paperback: 288
Pages
(2010-06-17)
list price: US$14.95 -- used & new: US$12.44 (price subject to change: see help) Asin: 0486422593 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
The best book for self teaching logic
Good coverage, but lack of solutions weakens it. Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more |
33. Mathematical Logic for Computer Science by Mordechai Ben-Ari | |
Kindle Edition: 304
Pages
(1992-12-31)
list price: US$54.95 Asin: B000V9GLTO Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
34. Friendly Introduction to Mathematical Logic, A by Christopher C. Leary | |
Hardcover: 218
Pages
(1999-12-08)
list price: US$76.00 -- used & new: US$50.00 (price subject to change: see help) Asin: 0130107050 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
Why is this out of print?
Most Accessible Undergraduate Text Covering Incompleteness |
35. First Order Mathematical Logic by Angelo Margaris | |
Paperback: 212
Pages
(1990-03-01)
list price: US$11.95 -- used & new: US$5.98 (price subject to change: see help) Asin: 0486662691 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (2)
I sat at the master's feet
First mathematical logic book I truly enjoyed! |
36. The Foundations of Mathematics (Logic) by Kenneth Kunen | |
Paperback: 262
Pages
(2009-09-08)
list price: US$24.75 -- used & new: US$22.27 (price subject to change: see help) Asin: 1904987141 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
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Kunen tales on indecidability of structures |
37. Introduction to Mathematical Structures and Proofs (Volume 0) by Larry J. Gerstein | |
Paperback: 364
Pages
(2008-06-13)
list price: US$23.00 -- used & new: US$19.75 (price subject to change: see help) Asin: 3540780440 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Good intro for beginning |
38. The Search for Mathematical Roots, 1870-1940 by I. Grattan-Guinness | |
Paperback: 624
Pages
(2001-01-15)
list price: US$85.00 -- used & new: US$57.37 (price subject to change: see help) Asin: 069105858X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since. Customer Reviews (3)
He hasn't yet given up on the 'paradoxes'
Not what you might expect
The best book of its kind in existence |
39. An Introduction to Fuzzy Logic for Practical Applications (Volume 0) by Kazuo Tanaka | |
Paperback: 148
Pages
(1996-11-15)
list price: US$159.00 -- used & new: US$104.39 (price subject to change: see help) Asin: 0387948074 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Excellent book!!!
A perfect intorduction to fuzzy logic
Good introduction, with some errors
Fast entry to notation
Breezy Intro to Fuzzy Logic |
40. From Symbolic Logic to Mathematical Logic by Silver | |
Hardcover: 400
Pages
(1993-07)
list price: US$24.95 -- used & new: US$29.00 (price subject to change: see help) Asin: 0697141756 Canada | United Kingdom | Germany | France | Japan | |
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