Abstract Set Theory

Abstract Set Theory PDF Author: Abraham Adolf Fraenkel
Publisher:
ISBN:
Category :
Languages : en
Pages : 297

Book Description


Abstract Set Theory

Abstract Set Theory PDF Author: Abraham Adolf Fraenkel
Publisher: Amsterdam : North-Holland Publishing Company
ISBN:
Category : Set theory
Languages : en
Pages : 316

Book Description


Foundations of Set Theory

Foundations of Set Theory PDF Author: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415

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.

Conceptions of Set and the Foundations of Mathematics

Conceptions of Set and the Foundations of Mathematics PDF Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255

Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Foundations of Point Set Theory

Foundations of Point Set Theory PDF Author: Robert Lee Moore
Publisher: American Mathematical Soc.
ISBN: 0821810138
Category : Mathematics
Languages : en
Pages : 434

Book Description


The Foundations of Mathematics in the Theory of Sets

The Foundations of Mathematics in the Theory of Sets PDF Author: John P. Mayberry
Publisher: Cambridge University Press
ISBN: 9780521770347
Category : Mathematics
Languages : en
Pages : 454

Book Description
This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory PDF Author: Douglas Cenzer
Publisher: World Scientific
ISBN: 9811201943
Category : Mathematics
Languages : en
Pages : 222

Book Description
This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.

Basic Set Theory

Basic Set Theory PDF Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 0486150739
Category : Mathematics
Languages : en
Pages : 418

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.

Defending the Axioms

Defending the Axioms PDF Author: Penelope Maddy
Publisher: Oxford University Press
ISBN: 0199596182
Category : Mathematics
Languages : en
Pages : 161

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.

Quine, New Foundations, and the Philosophy of Set Theory

Quine, New Foundations, and the Philosophy of Set Theory PDF Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 110715250X
Category : History
Languages : en
Pages : 221

Book Description
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.