Descriptive Set Theory and Forcing : How to Prove Theorems about Borel Sets the Hard Way (Hardcover)

1. What are the reals, anyway; Part I. On the Length of Borel Hierarchies: 2. Borel hierarchy; 3. Abstract Borel hierarchies; 4. Characteristic function of a sequence; 5. Martin's axiom; 6. Generic Gδ; 7. α-forcing; 8. Boolean algebras; 9. Borel order of a field of sets; 10. CH and orders of separable metric spaces; 11. Martin?Soloway theorem; 12. Boolean algebra of order ω1 ; 13. Luzin sets; 14. Cohen real model; 15. The random real model; 16. Covering number of an ideal; Part II. Analytic Sets: 17. Analytic sets; 18. Constructible well-orderings; 19. Hereditarily countable sets; 20. Schoenfield absoluteness; 21. Mansfield?Soloway theorem; 22. Uniformity and scales; 23. Martin's axiom and constructibility; 24. Σ12 well-orderings; 25. Large Π12 sets; Part III. Classical Separation Theorems: 26. Souslin?Luzin separation theorem; 27. Kleen separation theorem; 28. Π11 -reduction; 29. Δ11 -codes; Part IV. Gandy Forcing: 30. Π11 equivalence relations; 31. Borel metric spaces and lines in the plane; 32. Σ11 equivalence relations; 33. Louveau's theorem; 34. Proof of Louveau's theorem; References; Index; Elephant sandwiches.