Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

View: 3572

DOWNLOAD NOW »

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Set Theory and its Philosophy

A Critical Introduction

Author: Michael Potter

Publisher: Clarendon Press

ISBN: 0191556432

Category: Philosophy

Page: 360

View: 3740

DOWNLOAD NOW »

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.

Introduction to Logic

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486138054

Category: Mathematics

Page: 336

View: 3216

DOWNLOAD NOW »

Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.

The Philosophy of Set Theory

An Historical Introduction to Cantor's Paradise

Author: Mary Tiles

Publisher: Courier Corporation

ISBN: 0486138550

Category: Mathematics

Page: 256

View: 7098

DOWNLOAD NOW »

DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486497089

Category: Mathematics

Page: 256

View: 4551

DOWNLOAD NOW »

"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"--

An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

View: 4544

DOWNLOAD NOW »

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen,Martin Davis

Publisher: Courier Corporation

ISBN: 0486469212

Category: Mathematics

Page: 154

View: 6025

DOWNLOAD NOW »

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.

A Mathematical Prelude to the Philosophy of Mathematics

Author: Stephen Pollard

Publisher: Springer

ISBN: 3319058169

Category: Science

Page: 202

View: 9503

DOWNLOAD NOW »

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

Theory of Sets

Author: E. Kamke

Publisher: Courier Corporation

ISBN: 048645083X

Category: Mathematics

Page: 144

View: 2845

DOWNLOAD NOW »

This introduction to the theory of sets employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others. It analyzes concepts and principles, offering numerous examples. Topics include the rudiments of set theory, arbitrary sets and their cardinal numbers, ordered sets and their order types, and well-ordered sets and their ordinal numbers. 1950 edition.

Introduction to Logic

and to the Methodology of Deductive Sciences

Author: Alfred Tarski

Publisher: Courier Corporation

ISBN: 0486318893

Category: Mathematics

Page: 272

View: 1498

DOWNLOAD NOW »

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 5570

DOWNLOAD NOW »

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

View: 5804

DOWNLOAD NOW »

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Combinatorial Set Theory

With a Gentle Introduction to Forcing

Author: Lorenz J. Halbeisen

Publisher: Springer Science & Business Media

ISBN: 9781447121732

Category: Mathematics

Page: 456

View: 7768

DOWNLOAD NOW »

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Naive Set Theory

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 0486814874

Category: Mathematics

Page: 112

View: 4884

DOWNLOAD NOW »

Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.

Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

ISBN: 0486139646

Category: Mathematics

Page: 512

View: 4431

DOWNLOAD NOW »

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.

Introduction to Axiomatic Set Theory

Author: G. Takeuti,W.M. Zaring

Publisher: Springer Science & Business Media

ISBN: 1468499157

Category: Mathematics

Page: 251

View: 4342

DOWNLOAD NOW »

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.

Zermelo’s Axiom of Choice

Its Origins, Development, and Influence

Author: G.H. Moore

Publisher: Springer Science & Business Media

ISBN: 1461394783

Category: Mathematics

Page: 412

View: 708

DOWNLOAD NOW »

This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 4778

DOWNLOAD NOW »

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Set Theory

With an Introduction to Real Point Sets

Author: Abhijit Dasgupta

Publisher: Springer Science & Business Media

ISBN: 1461488540

Category: Mathematics

Page: 444

View: 5282

DOWNLOAD NOW »

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.