Abstract Set Theory
Title | Abstract Set Theory PDF eBook |
Author | Abraham Adolf Fraenkel |
Publisher | |
Total Pages | 316 |
Release | 1961 |
Genre | Set theory |
ISBN |
Foundations of Set Theory
Title | Foundations of Set Theory PDF eBook |
Author | A.A. Fraenkel |
Publisher | Elsevier |
Total Pages | 415 |
Release | 1973-12-01 |
Genre | Computers |
ISBN | 0080887058 |
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.
Set Theory and Logic
Title | Set Theory and Logic PDF eBook |
Author | Robert R. Stoll |
Publisher | Courier Corporation |
Total Pages | 512 |
Release | 2012-05-23 |
Genre | Mathematics |
ISBN | 0486139646 |
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Abstract Set Theory
Title | Abstract Set Theory PDF eBook |
Author | Abraham Adolf Fraenkel |
Publisher | |
Total Pages | 297 |
Release | 1968 |
Genre | |
ISBN |
A Book of Set Theory
Title | A Book of Set Theory PDF eBook |
Author | Charles C Pinter |
Publisher | Courier Corporation |
Total Pages | 259 |
Release | 2014-07-23 |
Genre | Mathematics |
ISBN | 0486497089 |
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Abstract Set Theory; 8
Title | Abstract Set Theory; 8 PDF eBook |
Author | Th (Thoralf) 1887-1963 Skolem |
Publisher | Hassell Street Press |
Total Pages | 88 |
Release | 2021-09-09 |
Genre | |
ISBN | 9781014083531 |
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Classic Set Theory
Title | Classic Set Theory PDF eBook |
Author | D.C. Goldrei |
Publisher | Routledge |
Total Pages | 296 |
Release | 2017-09-06 |
Genre | Mathematics |
ISBN | 1351460617 |
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.