The Axiom of Choice - Paperback

The Axiom of Choice by Thomas J. Jech

This comprehensive textbook provides an in-depth examination of the axiom of choice and its fundamental role in set theory and mathematical logic. Written by Thomas J. Jech and published by Dover Publications, this self-contained text serves as an essential resource for graduate students and researchers studying advanced mathematical foundations.

Comprehensive Coverage of Set Theory

The text systematically explores the relative strengths and consequences of the axiom of choice through carefully structured chapters. Beginning with an introduction to the use of the axiom of choice, the book progresses through explorations of consistency, permutation models, and independence. Each chapter builds upon previous concepts to provide a thorough understanding of this central principle in mathematical logic.

Advanced Topics and Theorems

Subsequent chapters examine embedding theorems, models with finite supports, and weaker versions of the axiom. The book also investigates nontransferable statements and their implications. Final sections consider mathematics without choice, exploring how mathematical systems function in the absence of this axiom. The text addresses cardinal numbers in set theory without choice and examines properties that contradict the axiom of choice, including detailed coverage of the axiom of determinacy and related topics.

Structured Learning Approach

Each chapter contains several problems graded according to difficulty, allowing readers to test their understanding and develop problem-solving skills progressively. Historical remarks conclude each chapter, providing context for the development of these mathematical concepts and connecting theoretical foundations to their evolution within the field.

Ideal for Graduate Study and Self-Study

This Dover Books on Mathematics publication is designed for graduate-level study and serves equally well for self-directed learning. The self-contained nature of the text means readers can work through the material independently while gaining a rigorous understanding of the axiom of choice and its implications for modern mathematics and logic.

Published as a paperback edition in August 2008, this textbook represents an authoritative treatment of set theory fundamentals, making complex mathematical logic accessible to serious students of mathematics and philosophy of mathematics.