Offers an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). This title describes the classical theory developed by Bernstein, Cantor, Hausdorff, Konig and Tarski between 1870 and 1930.
One of the greatest revolutions in mathematics occurred when Georg Cantor promulgated his theory of transfinite sets. His religious beliefs led him to expect paradoxes in any concept of the infinite. This work shows that these played an integral part in his understanding and defense of set theory.
Helps you in understanding set theory and related topics. This study tool takes you step-by-step through the subject and gives you 530 accompanying related problems with fully worked solutions. It also features problems in the ordinals, cardinals, and transfinite series chapters, and a coverage of real numbers and integers.
A text for mathematics courses that covers the basics such as relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It includes material on normal forms and Goodstein sequences. It provides important ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.
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.
Set theory has become one of the most respected fields in mathematics due to the situation in which sets are used to build mathematical structures, pervading the whole of modern mathematics, and objects. This book presents and discusses research in the study of set theory, as well as their role and place in mathematics.
Offering a philosophical introduction to set theory, this book interweaves a presentation of the technical material with a philosophical critique. At every stage, it discusses the reasons that can be offered for believing it to be true. It is designed as a key text for philosophy, mathematical logic, and computer science.
This 'excursion' through the evolution of research mathematics takes in some 40 papers, published up to the 1970s, on proofs of the Cantor-Bernstein theorem. It provides a detailed example of proof-processing in the derivation of Bernstein's division theorem.
Praise for the First Edition "... an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity. "--Computing Reviews "... a very well written introduction to set theory... easy to read and well suited for self-study... highly recommended.