"Graduate Set Theory Notes" Webpage

Graduate Set Theory Notes
Set Theory, The Third Millennium Edition, Revised and Expanded, by Thomas Jech (Springer-Verlag 1997, revised and corrected 2006) Jech's Set Theory, The Third Millenium Edition book

Jech's Set Theory, The Third Millenium Edition book

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).

Part I. Basic Set Theory

Section 1. Axioms of Set Theory.
Section 2. Ordinal Numbers.
Section 3. Cardinal Numbers.
Section 4. Real Numbers.
Section 5. The Axiom of Choice and Cardinal Arithmetic.
Section 6. The Axiom of Regularity.
Section 7. Filters, Ultrafilters and Boolean Algebras.
Section 8. Stationary Sets.
Section 9. Combinatorial Set Theory.
Section 10. Measurable Cardinals.
Section 11. Borel and Analytic Sets.
Section 12. Models of Set Theory.

Part II. Advanced Set Theory

Section 13. Constructible Sets.
Section 14. Forcing.
Section 15. Applications of Forcing.
Section 16. Iterated Forcing and Martin's Axiom.
Section 17. Large Cardinals.
Section 18. Large Cardinals and L.
Section 19. Iterated Ultrapowers and L[U].
Section 20. Very Large Cardinals.
Section 21. Large Cardinals and Forcing.
Section 22. Saturated Ideals.
Section 23. The Nonstationary Ideal.
Section 24. The Singular Cardinal Problem.
Section 25. Descriptive Set Theory.
Section 26. The Real Line.

Part III. Selected Topics

Section 27. Combinatorial Principles in L.
Section 28. More Applications of Forcing.
Section 29. More Combinatorial Set Theory.
Section 30. Complete Boolean Algebras.
Section 31. Proper Forcing.
Section 32. More Descriptive Set Theory.
Section 33. Determinancy.
Section 34. Supercompact Cardinals and the Real Line.
Section 35. Inner Models for Large Cardinals.
Section 36. Forcing and Large Cardinals.
Section 37. Martin's Maximum.
Section 38. More on Stationary Sets.

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