Foundations of Set Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Foundations of Set Theory PDF full book. Access full book title Foundations of Set Theory by A.A. Fraenkel. Download full books in PDF and EPUB format.
Author: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415
Get Book Here
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: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415
Get Book Here
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: Abraham Adolf Fraenkel
Publisher:
ISBN:
Category :
Languages : en
Pages : 297
Get Book Here
Book Description
Author: Abraham Adolf Fraenkel
Publisher: Amsterdam : North-Holland Publishing Company
ISBN:
Category : Set theory
Languages : en
Pages : 316
Get Book Here
Book Description
Author: Robert Lee Moore
Publisher: American Mathematical Soc.
ISBN: 0821810138
Category : Mathematics
Languages : en
Pages : 434
Get Book Here
Book Description
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
Get Book Here
Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 110715250X
Category : History
Languages : en
Pages : 221
Get Book Here
Book Description
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author: John P. Mayberry
Publisher: Cambridge University Press
ISBN: 9780521770347
Category : Mathematics
Languages : en
Pages : 454
Get Book Here
Book Description
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418
Get Book Here
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: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199596182
Category : Mathematics
Languages : en
Pages : 161
Get Book Here
Book Description
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.
Author: F. William Lawvere
Publisher: Cambridge University Press
ISBN: 9780521010603
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
