Sets and Transfinite Algebra

Name: Sets and Transfinite Algebra
Price: 86.53 AUD
Availability: OutOfStock
ISBN: 9781009737876

Thomas Müller (Universität Wien, Austria)

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English

Cambridge University Press
09 April 2026

Mathematical logic; Set theory; Algebra

Series: London Mathematical Society Student Texts

This two-part book offers a rigorous yet accessible exploration of set theory and transfinite algebra, with a particular emphasis on the axiom of choice and its applications. Part I presents an informal axiomatic introduction to the foundations of set theory, including a detailed treatment of the axiom of choice and its equivalents, suitable for advanced undergraduates. Part II, aimed at graduate students and professional mathematicians, treats selected topics in transfinite algebra where the axiom of choice, in one form or another, is useful or even indispensable. The text features self-contained chapters for flexible use, and includes material rarely found in the literature, such as Tarski's work on complete lattices, Hamel's solution to Cauchy's functional equation, and Artin's resolution of Hilbert's 17th problem. Over 140 exercises, with full solutions provided in the Appendix, support active engagement and deeper understanding, making this a valuable resource for both independent study and course preparation.

By: Thomas Müller (Universität Wien Austria)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Weight: 323g
ISBN: 9781009737876
ISBN 10: 1009737872
Series: London Mathematical Society Student Texts
Pages: 218
Publication Date: 09 April 2026
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Thomas Müller, formerly of Queen Mary & Westfield College (London), is affiliated with the University of Vienna as a Professorial Research Fellow in the Department of Mathematics. His main research interests are in the areas of algebra, combinatorics, and geometry. He is the co-author of 'A Universal Construction for Groups Acting Freely on Real Trees' (2012).