Author: K. J. Devlin
Publisher: Springer
ISBN: 354037034X
Category : Mathematics
Languages : en
Pages : 105

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Book Description

Author: K. J. Devlin
Publisher:
ISBN: 9783662204320
Category :
Languages : en
Pages : 108

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Author: Lev D. Beklemishev
Publisher: Elsevier
ISBN: 9780080955001
Category : Mathematics
Languages : en
Pages : 634

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Provability, Computability and Reflection

Author: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415

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Book Description
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.

Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362

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Book Description
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: Herbert Popp
Publisher:
ISBN: 9780387071473
Category : Algebraic varieties
Languages : en
Pages : 358

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Author: Frederick Rowbottom
Publisher:
ISBN:
Category : Processes, Infinite
Languages : en
Pages : 164

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Author: Keith J. Devlin
Publisher: Cambridge University Press
ISBN: 1316739422
Category : Mathematics
Languages : en
Pages : 439

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Book Description
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the Lα-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the Jα-hierarchy and the Jensen 'fine-structure theory'.

Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418

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Book Description
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.

Author: G. Takeuti
Publisher: Springer Science & Business Media
ISBN: 1468499157
Category : Mathematics
Languages : en
Pages : 255

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Book Description
In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. For our slow development we claim the following advantages. The text is one from which a student can learn with little supervision and instruction. This enables the instructor to use class time for the presentation of alternative developments and supplementary material.