The Foundations of Mathematics in the Theory of Sets

The Foundations of Mathematics in the Theory of Sets
Author: John P. Mayberry
Publisher: Cambridge University Press
Total Pages: 454
Release: 2000
Genre: Mathematics
ISBN: 9780521770347

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.

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
Author: Douglas Cenzer
Publisher: World Scientific
Total Pages: 222
Release: 2020-04-04
Genre: Mathematics
ISBN: 9811201943

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.

Reflections on the Foundations of Mathematics

Reflections on the Foundations of Mathematics
Author: Stefania Centrone
Publisher: Springer Nature
Total Pages: 511
Release: 2019-11-11
Genre: Mathematics
ISBN: 3030156559

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Introduction to the Theory of Sets

Introduction to the Theory of Sets
Author: Joseph Breuer
Publisher: Courier Corporation
Total Pages: 130
Release: 2012-08-09
Genre: Mathematics
ISBN: 0486154874

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

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"--

Sets for Mathematics

Sets for Mathematics
Author: F. William Lawvere
Publisher: Cambridge University Press
Total Pages: 280
Release: 2003-01-27
Genre: Mathematics
ISBN: 9780521010603

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Labyrinth of Thought

Labyrinth of Thought
Author: Jose Ferreiros
Publisher: Springer Science & Business Media
Total Pages: 472
Release: 2001-11-01
Genre: Mathematics
ISBN: 9783764357498

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)