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Author: Stephen Pollard
Publisher: Courier Dover Publications
Published: 2015-07-15
Total Pages: 196
ISBN-13: 0486797147
DOWNLOAD EBOOK →This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
Author: Michael Potter
Publisher: Clarendon Press
Published: 2004-01-15
Total Pages: 362
ISBN-13: 0191556432
DOWNLOAD EBOOK →Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author: Mary Tiles
Publisher: Courier Corporation
Published: 2012-03-08
Total Pages: 258
ISBN-13: 0486138550
DOWNLOAD EBOOK →DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Author: Paul J. Cohen
Publisher: Courier Corporation
Published: 2008-12-09
Total Pages: 196
ISBN-13: 0486469212
DOWNLOAD EBOOK →This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Author: John P. Burgess
Publisher: Cambridge University Press
Published: 2022-02-28
Total Pages: 75
ISBN-13: 9781108986915
DOWNLOAD EBOOK →Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
Author: Michael D. Potter
Publisher: Clarendon Press
Published: 2004
Total Pages: 345
ISBN-13: 9780199269730
DOWNLOAD EBOOK →A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
Author: Willard Van Orman Quine
Publisher: Harvard University Press
Published: 1969
Total Pages: 381
ISBN-13: 0674802071
DOWNLOAD EBOOK →This is an extensively revised edition of W. V. 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.
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 696
ISBN-13:
DOWNLOAD EBOOK →Author: Luca Incurvati
Publisher: Cambridge University Press
Published: 2020-01-23
Total Pages: 255
ISBN-13: 1108497829
DOWNLOAD EBOOK →Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Winfried Just
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 210
ISBN-13: 0821802666
DOWNLOAD EBOOK →This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
