Axiom of Choice

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.

Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results.

This book provides a first course in set theory suitable for final year undergraduates in mathematics. The book develops the subject from first principles and presupposes little more than an elementary grounding in logic.

by Ernst-Erich Doberkat (Author)
Provides a systematic and accessible treatment of useful topics for theoretical computer scientists
Displays the mathematical techniques with carefully constructed and rigorous approaches
Includes a variety of examples from diverse fields of mathematics and computer science
Features case studies to provide methods for research problems
Classroom tested exposition of the content

This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas.

This is the first comprehensive collection of problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period between 1920-1970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis.

This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems. Using motivations, rigorous definitions, proofs and various examples, the author systematically introduces the Axiom of Choice, explains Banach-Mazur games and the Axiom of Determinacy, discusses the basic constructions of sets and the interplay of coalgebras and Kripke models for modal logics with an emphasis on Kleisli categories, monads and probabilistic systems.