Set Theory [Paperback]

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. It is based in large part on courses given over many years by Professor Hajnal, which have been brought up to date wherever necessary. The first part is elementary, and is designed to introduce all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. It is based in large part on courses given over many years by Professor Hajnal, which have been brought up to date wherever necessary. The first part is elementary, and is designed to introduce all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. Providing complete, up-to-date coverage, the book is based in large part on courses given over many years by Professor Hajnal. The first part introduces all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.Part I. Introduction to Set Theory: 1. Notation, conventions; 2. Definition of equivalence. The concept of cardinality. The axiom of choice; 3. Countable cardinal, continuum cardinal; 4. Comparison of cardinals; 5. Operations with sets and cardinals; 6. Examples; 7. Ordered sets. Order types. Ordinals; 8. Properties of well-ordered sets. Good sets. The ordinal operation; 9. Transfinite induction and recursion; 10. DelS(