Classic Set Theory for Guided Independent Study

Taking a modern perspective on this classical subject, this textbook supplies students with sufficient grounding in a rigorous approach to the revolutionary results of set theory and enables them to tackle significant problems that arise from the theory. It assumes some experience with using sets, function, basic logic, and the fundamentals of real analysis. Specifically designed for self-study, the text provides a wealth of exercises that range from routine practice problems to rather difficult ones, including some without clear-cut answers that are intended to spark debate. It includes full solutions to many of the exercises.

Informationen zum Autor Goldrei, D.C. Klappentext Taking a modern perspective on this classical subject, this textbook supplies students with sufficient grounding in a rigorous approach to the revolutionary results of set theory and enables them to tackle significant problems that arise from the theory. It assumes some experience with using sets, function, basic logic, and the fundamentals of real analysis. Specifically designed for self-study, the text provides a wealth of exercises that range from routine practice problems to rather difficult ones, including some without clear-cut answers that are intended to spark debate. It includes full solutions to many of the exercises. Zusammenfassung Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory. Inhaltsverzeichnis Preface, 1 Introduction, 2 The Real Numbers, 3 The Natural Numbers, 4 The Zermelo-Fraenkel Axioms, 5 The Axiom of Choice, 6 Cardinals (without the Axiom of Choice), 7 Ordered Sets, 8 Ordinal Numbers, 9 Set Theory with the Axiom of Choice, Bibliography, Index

Autorentext

Goldrei, D.C.

Zusammenfassung
Designed for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory.

Inhalt
Preface, 1 Introduction, 2 The Real Numbers, 3 The Natural Numbers, 4 The Zermelo-Fraenkel Axioms, 5 The Axiom of Choice, 6 Cardinals (without the Axiom of Choice), 7 Ordered Sets, 8 Ordinal Numbers, 9 Set Theory with the Axiom of Choice, Bibliography, Index