The Best Set Theory Books for Beginners

Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.

Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable. The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory.

Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.

Set Theory for Beginners consists of a series of basic to intermediate lessons in set theory. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for. professors teaching an undergraduate course or basic graduate course in set theoryhigh school teachers working with advanced math studentsstudents wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes:. 16 lessons consisting of basic to intermediate topics in set theory and mathematical logic.

A problem set after each lesson arranged by difficulty level.A complete solution guide is included as a downloadable PDF file. Set Theory Book Table Of Contents (Selected). Here's a selection from the table of contents:. Introduction. Lesson 1 - Sets. Lesson 2 - Subsets. Lesson 3 - Operations on Sets. Lesson 4 - Relations. Lesson 5 - Equivalence Relations and Partitions. Lesson 6 - Functions. Lesson 7 - Equinumerosity. Lesson 8 - Induction and Recursion on N. Lesson 9 - Propositional Logic. Lesson 10 - First-order Logic. Lesson 11 - Axiomatic Set Theory. Lesson 12 - Ordinals. Lesson 13 - Cardinals. Lesson 14 - Martin's Axiom. Lesson 15 - The Field of Real Numbers. Lesson 16 - Clubs and Stationary Sets.