A Book of Set Theory

A Book of Set Theory
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"--

Set Theory and its Philosophy

Set Theory and its Philosophy
Author: Michael Potter
Publisher: Clarendon Press
Total Pages: 362
Release: 2004-01-15
Genre: Philosophy
ISBN: 0191556432

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.

Classic Set Theory

Classic Set Theory
Author: D.C. Goldrei
Publisher: Routledge
Total Pages: 300
Release: 2017-09-06
Genre: Mathematics
ISBN: 1351460609

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.

Set Theory and the Continuum Hypothesis

Set Theory and the Continuum Hypothesis
Author: Paul J. Cohen
Publisher: Courier Corporation
Total Pages: 196
Release: 2008-12-09
Genre: Mathematics
ISBN: 0486469212

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Set Theory: The Structure of Arithmetic

Set Theory: The Structure of Arithmetic
Author: Norman T. Hamilton
Publisher: Courier Dover Publications
Total Pages: 289
Release: 2018-05-16
Genre: Mathematics
ISBN: 0486830470

This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Elements of Set Theory

Elements of Set Theory
Author: Herbert B. Enderton
Publisher: Academic Press
Total Pages: 294
Release: 1977-05-23
Genre: Mathematics
ISBN: 0080570429

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Set Theory and Logic

Set Theory and Logic
Author: Robert R. Stoll
Publisher: Courier Corporation
Total Pages: 516
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.

Naive Set Theory

Naive Set Theory
Author: Paul Halmos
Publisher:
Total Pages: 98
Release: 2019-06
Genre:
ISBN: 9781950217014

Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org