Basic Set Theory

Erscheinungsjahr 2026
ISBN: 978-3-032-38883-4
Verlag: Springer

Buch, Englisch, 186 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Springer Undergraduate Mathematics Series

This book provides a rigorous, step-by-step, and detailed introduction to axiomatic set theory within the standard framework of Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC). It is suitable as a textbook for a one-semester course in set theory at the senior undergraduate or first-year graduate level.

Although the presentation is self-contained, the text is best suited for students in mathematics, philosophy, computer science, or linguistics who have some prior background in logic. The book covers all standard material, including a thorough construction of the natural numbers and the linear continuum, followed by the basic theory of transfinite ordinals and cardinals, and concluding with an overview of the general structure of the set-theoretic universe. Each chapter begins with an introduction and ends with a carefully designed set of exercises aimed at reinforcing the material and developing proof-writing skills.

Based on a course taught by the authors at the University of Barcelona over the past 12 years, the book has been refined over time to ensure clarity and accessibility. In addition to serving as a course textbook, it contains the core material in set theory typically required by working mathematicians, so can also be used as a reference for mathematicians and mathematically inclined philosophers.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Bagaria, Joan

Jané, Ignasi

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre

Inhaltsverzeichnis

Chapter 1. Introduction.- Chapter 2. The First Axioms.- Chapter 3. The Natural Numbers.- Chapter 4. Countable Sets.- Chapter 5. The Linear Continuum.- Chapter 6. Well-Orders.- Chapter 7. Ordinals.- Chapter 8. Cardinal Comparability and the Axiom of Choice.- Chapter 9. Infinite Cardinals.- Chapter 10. The Cumulative Hierarchy.- Chapter 11. Classes.The Theory NBG.

Über Autor(innen)

Joan Bagaria is a UC Berkeley PhD in Logic, holding, since 2001, a prestigious ICREA Research Professorship at Univ of Barcelona (UB). He has over 60 publications and has delivered over 90 invited talks at international conferences, including the ASL Gödel lecture. He has directed 11 PhD theses and been coordinator and PI of the Logic Group at UB since 2002. He was elected first President of the European Set Theory Society and was awarded the Simons Fellowship at INI (Cambridge).

Ignasi Jané was a professor of Logic at University of Barcelona. He retired in 2015. His research was on the philosophy of logic and mathematics. He taught undergraduate and master's courses in Logic and Set Theory at UB for over 30 years. His book (co-authored) entitled "Elementos de lógica formal" (in Spanish), published in 2007, has been widely used as a textbook in Logic in Spain and Latin America.