Introduction to Set Theory Notes
Introduction to Set Theory, Second Edition Revised and Expanded, by Karel Hrbacek and Thomas Jech, Dekker (1984).
Hrbacek and Jech's Introduction to Set Theory book, 2nd edition

Introduction to Set Theory is not a formal ETSU class (sadly). This would be a cross-listed 4000/5000 level class with potential catalog description: "Covers the standard topics of a first class in axiomatic set theory. Topics include equivalence relations, orderings, cardinalities and cardinal numbers, axiomatic development of the natural and real numbers, ordinal numbers, the Zermelo axioms of set theory, and the Axiom of Choice." The prerequisite is Mathematical Reasoning (MATH 3000). Introduction to Set Theory would be a prerequisite to the (graduate-only level) Set Theory class, for which I have online notes at Graduate Set Theory (these notes are still at the planning stage, as of Fall 2022).

Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results which are particularly lengthy (shorter proofs are contained in the notes themselves). The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

  1. Chapter 1. Sets.
  2. Chapter 2. Relations, Functions, and Orderings.
  3. Chapter 3. Natural Numbers.
  4. Chapter 4. Finite and Countable Sets.
  5. Chapter 5. Real Numbers.
  6. Chapter 6. Cardinal Numbers.
  7. Chapter 7. Ordinal Numbers.
  8. Chapter 8. Alephs.
  9. Chapter 9. The Axiom of Choice.
  10. Chapter 10. Arithmetic of Cardinal Numbers.
  11. Chapter 11. Uncountable Sets.
  12. Chapter 12. The Axiomatic Set Theory.

Chapter 1. Sets.

Chapter 2. Relations, Functions, and Orderings.

Chapter 3. Natural Numbers.

Chapter 4. Finite and Countable Sets.

Chapter 5. Real Numbers.

Chapter 6. Cardinal Numbers.

Chapter 7. Ordinal Numbers.

Chapter 8. Alephs.

Chapter 9. The Axiom of Choice.

Chapter 10. Arithmetic of Cardinal Numbers.

Chapter 11. Uncountable Sets.

Chapter 12. The Axiomatic Set Theory.


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