The Axiom of Constructibility
Author: K. J. Devlin
Publisher: Springer
Published: 2006-11-15
Total Pages: 105
ISBN-13: 354037034X
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Author: K. J. Devlin
Publisher: Springer
Published: 2006-11-15
Total Pages: 105
ISBN-13: 354037034X
DOWNLOAD EBOOKAuthor: K. J. Devlin
Publisher:
Published: 2014-09-01
Total Pages: 108
ISBN-13: 9783662204320
DOWNLOAD EBOOKAuthor: Herbert Popp
Publisher:
Published: 1977
Total Pages: 358
ISBN-13: 9780387071473
DOWNLOAD EBOOKAuthor: Richard L. Poss
Publisher:
Published: 1970
Total Pages: 198
ISBN-13:
DOWNLOAD EBOOKAuthor: Frederick Rowbottom
Publisher:
Published: 1964
Total Pages: 164
ISBN-13:
DOWNLOAD EBOOKAuthor: C. Alkor
Publisher:
Published: 1982
Total Pages: 44
ISBN-13:
DOWNLOAD EBOOKAuthor: J.L. Krivine
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 108
ISBN-13: 9401031444
DOWNLOAD EBOOKThis book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods. Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point. Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work (2 cycle de mathernatiques).
Author: Lev D. Beklemishev
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 281
ISBN-13: 0080957765
DOWNLOAD EBOOKConstructible Sets with Applications
Author: Lev D. Beklemishev
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 684
ISBN-13: 0080955002
DOWNLOAD EBOOKFoundational Studies Selected Works
Author: Michael Potter
Publisher: Clarendon Press
Published: 2004-01-15
Total Pages: 362
ISBN-13: 0191556432
DOWNLOAD EBOOKMichael 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.