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1. Logic and set theory: With applications by Philip M Cheifetz | |
Paperback: 469
Pages
(2004)
Isbn: 0916060071 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
2. Set Theory and Logic by Robert R. Stoll | |
Paperback: 496
Pages
(1979-10-01)
list price: US$19.95 -- used & new: US$9.99 (price subject to change: see help) Asin: 0486638294 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Good for self-study or nonmajors
Very Terse Treatment of a Broad Range of Topics
Incredible Best Buy Intuitive set theory through the axiom of choice (Halmos) Natural numbers Æ Integers Æ Rationals Æ Reals (Feferman) Mathematical logic (Machover, Smullyan) Metamathetics (Machover, Mendelson) Introduction to the axiomatic approach ZF axiomatic set theory (Suppes) Boolean algebra through Stone's theorem and the completeness of sentential logic (Halmos & Givant) Algebra (Birkhoff & MacLane's "Algebra") Stoll's style is quite discursive, far from the terse lemma-theorem-corollary-remark style of so much 20th century mathematics. My only major disappointment is that the formal proof technique set out in chpt. 4 is natural deduction rather than the tableau method or Quine's Main Method. It is indeed the case that there are no solutions to the exercises, but I do not believe that that is a major flaw.
Unusually clear treatment of very abstract matters.
Good book that falls short of being a great book. |
3. Set Theory, Logic and their Limitations by Moshe Machover | |
Paperback: 300
Pages
(1996-05-31)
list price: US$43.00 -- used & new: US$33.94 (price subject to change: see help) Asin: 0521479983 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
An excellent introduction to mathematical logic |
4. Set Theory and Its Logic, Revised Edition by W. V. Quine | |
Paperback: 380
Pages
(1969-01-01)
list price: US$30.50 -- used & new: US$16.88 (price subject to change: see help) Asin: 0674802071 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted. Customer Reviews (1)
Masterwork |
5. Lectures in Logic and Set Theory: Volume 2, Set Theory (Cambridge Studies in Advanced Mathematics) by George Tourlakis | |
Paperback: 591
Pages
(2010-09-09)
list price: US$70.00 -- used & new: US$70.00 (price subject to change: see help) Asin: 0521168481 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Excellent book as an advanced introduction. |
6. Notes on Logic and Set Theory (Cambridge Mathematical Textbooks) by P. T. Johnstone | |
Paperback: 124
Pages
(1987-10-30)
list price: US$39.99 -- used & new: US$24.99 (price subject to change: see help) Asin: 0521336929 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (8)
Good On the other hand, for people with *some* background and *some*mathematical inclination and *some* sense of mathematical beauty, this bookis fun. The abstract approach brings out the essential features of thenotions studied in logic, provides slick proofs and makes an implicit casefor the unity of mathematics including mathematical logic -- which is themathematical study of (various aspects of) mathematics itself. I personallylike these "abstractions" but if you don't like them or if youdon't yet have the necessary background, don't worry: There are other goodlogic books out there with a lighter touch.
Nice (algebraic) introduction On the other hand, for people with *some* background and *some*mathematical inclination and *some* sense of mathematical beauty, this bookis fun. The abstract approach brings out the essential features of thenotions studied in logic, provides slick proofs and makes an implicit casefor the unity of mathematics including mathematical logic -- which is themathematical study of (various aspects of) mathematics itself. I personallylike these "abstractions" but if you don't like them or if youdon't yet have the necessary background, don't worry: There are other goodlogic books out there with a lighter touch.
interesting book Not very suitable for introduction. But good nevertheless. I esp. like the section on computability. The logic and set theory were a bit too short. I agree with the Vera Suslova thatthis is not for beginners!
Good On the other hand, for people with *some* background and *some*mathematical inclination and *some* sense of mathematical beauty, this bookis fun. The abstract approach brings out the essential features of thenotions studied in logic, provides slick proofs and makes an implicit casefor the unity of mathematics including mathematical logic -- which is themathematical study of (various aspects of) mathematics itself. I personallylike these "abstractions" but if you don't like them or if youdon't yet have the necessary background, don't worry: There are other goodlogic books out there with a lighter touch.
Good On the other hand, for people with *some* background and *some*mathematical inclination and *some* sense of mathematical beauty, this bookis fun. The abstract approach brings out the essential features of thenotions studied in logic, provides slick proofs and makes an implicit casefor the unity of mathematics including mathematical logic -- which is themathematical study of (various aspects of) mathematics itself. I personallylike these "abstractions" but if you don't like them or if youdon't yet have the necessary background, don't worry: There are other goodlogic books out there with a lighter touch. ... Read more |
7. Lectures in Logic and Set Theory: Volume 1, Mathematical Logic (Cambridge Studies in Advanced Mathematics) by George Tourlakis | |
Paperback: 342
Pages
(2010-09-09)
list price: US$40.00 -- used & new: US$36.00 (price subject to change: see help) Asin: 0521168465 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
8. The Structure of Proof: With Logic and Set Theory by Michael O'Leary | |
Hardcover: 418
Pages
(2002-01-15)
list price: US$111.00 -- used & new: US$99.00 (price subject to change: see help) Asin: 0130190772 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A brilliant textbook by a brilliant Professor |
9. Introduction to Mathematical Logic: Set Theory - Computable Functions - Model Theory (Undergraduate Texts in Mathematics) by Jerome Malitz | |
Hardcover: 198
Pages
(1979-05-01)
list price: US$49.95 -- used & new: US$48.90 (price subject to change: see help) Asin: 0387903461 Canada | United Kingdom | Germany | France | Japan | |
10. Algebra, Logic, Set Theory (Studies in Logic) | |
Hardcover: 324
Pages
(2007-01-01)
list price: US$49.50 -- used & new: US$49.49 (price subject to change: see help) Asin: 1904987281 Canada | United Kingdom | Germany | France | Japan | |
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11. Foundations of analysis,: With an introduction to logic and set theory (The Appleton-Century mathematics series) by D. A. Clarke, B. Brainerd | |
Hardcover: 363
Pages
(1971)
-- used & new: US$67.73 (price subject to change: see help) Asin: 0390197564 Canada | United Kingdom | Germany | France | Japan | |
12. Fuzzy Sets and Fuzzy Logic: Theory and Applications by George J. Klir, Bo Yuan | |
Hardcover: 592
Pages
(1995-05-21)
list price: US$101.00 -- used & new: US$44.36 (price subject to change: see help) Asin: 0131011715 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
Not just fuzzy
Care is needed
First bible of fuzzy systems theory since Dubois and Prade. Theapplications section presents theory which could be useful in applicationsrather than the applications themselves. References are given, but nodistinction is made between theoretical work and real-world applications,and many of the references are old and out-of-date. For a reference bookon fuzzy mathematics, this book is superb; as a pointer to real-worldapplications, it leaves something to be desired.
Robust treatment of fuzzy logic has interdisciplinary appeal
One of the most important book to learn about fuzzy logic |
13. Trading Ontology for Ideology: The Interplay of Logic, Set Theory and Semantics in Quine's Philosophy (Synthese Library) by L. Decock | |
Hardcover: 288
Pages
(2002-09-30)
list price: US$149.00 -- used & new: US$118.31 (price subject to change: see help) Asin: 1402008651 Canada | United Kingdom | Germany | France | Japan | |
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14. Boolean-Valued Models and Independence Proofs in Set Theory (Oxford Logic Guides) by John Lane Bell | |
Hardcover: 165
Pages
(1985-08-15)
list price: US$26.00 -- used & new: US$59.00 (price subject to change: see help) Asin: 0198532415 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (1)
THE book for studying Boolean-valued models of set theory Nonetheless, you may one day find that you need the Boolean algebra approach. This was the approach developed by Scott and Solovay after Cohen's somewhat inscrutable approach to proving the consistency of not-CH had been adequately digested. The Boolean algebra approach isvery elegant and algebraic, and the theorems are often bettermotivated than they are in the partial orders approach. When I was a graduate student, I studied both approaches,but eventually forgot much of what I learned about Boolean-valued models because in practice I always relied on the other approach. Recently, however, in some research I've been doing in an extension of ZFC in an extended language, I found that some of the usual assumptions one can make in doing forcing over ZFC models were no longer applicable in the new setting. Without going into the details, the consequence was that I had to do forcing over non-wellfounded models of ZFC and examine the properties of the resulting forcing extension, perhaps iterating the process omega many times. The only way to do this has been to work with Boolean-valued models M^B of the non-wellfounded ground model M, prove the desired properties within M^B, then collapse with a generic ultrafilter, and go on to the next model. Well, after that long-winded introduction, my point is this: Bell's treatment of Boolean-valued models is outstanding. I have several of Bell's books and his talent as an expositor is his relentless attention to detail. He does no hand-waving. If you need to face the details of Boolean-valued models, Bell's approach is the right way to go. In the first chapter he develops the theory enough to prove that all ZFC axioms hold in V^B. In Chapter 2 he shows how to do independence proofs in Boolean valued models -- illustrating with CH and developing the usual results about chain conditions and distributivity, never once working with a 2-valued forcing extension. The third chapter reveals some of the elegance of the Boolean algebra approach in its development of the proof of the consistency of not-AC using group actions. Chapter 4 shows how to get the usual results about forcing involving 2-valued models by considering (V^B)/U, where U is a generic ultrafilter. Chapter 5 is a special chapter about cardinal collapsing, introduced because the Boolean algebras introduced before always preserved cardinals and cofinalities. Finally, chapter 6, which was added in the 1985 edition, treats iterated forcing. This chapter contains details that appear nowhere else and are very handy if you need to deal with such things. As ever, Bell has done a thorough job in his treatment of this subject. It is the right reference for Boolean-valued models of set theory. ... Read more |
15. A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns by Piero Pagliani | |
Paperback: 788
Pages
(2009-12-28)
list price: US$469.00 -- used & new: US$469.00 (price subject to change: see help) Asin: 9048179351 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description 'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost. Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields. 'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets. |
16. Set Theory and Logic by A.A. Fraenkel | |
Hardcover: 102
Pages
(1967-01)
list price: US$8.95 Isbn: 0201020858 Canada | United Kingdom | Germany | France | Japan | |
17. Foundations of Computing: System Development With Set Theory and Logic (International Computer Science Series) by Thierry Scheurer | |
Paperback: 668
Pages
(1994-07)
list price: US$63.00 Isbn: 0201544296 Canada | United Kingdom | Germany | France | Japan | |
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18. Sets, Logic and Axiomatic Theories by Robert R. Stoll | |
Hardcover: 233
Pages
(1975-01-13)
Isbn: 0716704579 Canada | United Kingdom | Germany | France | Japan | |
19. Elements of Mathematical Logic and Set Theory by J & Borkowski, L Slupecki | |
Hardcover: 362
Pages
(1967)
Isbn: 0080110967 Canada | United Kingdom | Germany | France | Japan | |
20. Problems in Set Theory, Mathematical Logic and the Theory of Algorithms (University Series in Mathematics) by Igor Lavrov, Larisa Maksimova | |
Hardcover: 302
Pages
(2003-03-01)
list price: US$185.00 -- used & new: US$132.06 (price subject to change: see help) Asin: 0306477122 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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