These notes develop the theory of deillegalscriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.
Über den Autor
Arnold W. Miller works in the Department of Mathematics at the University of Wisconsin, Madison.
Inhaltsverzeichnis
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 G¿; 7. ¿-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 ¿1 ; 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. ¿12 well-orderings; 25. Large ¿12 sets; Part III. Classical Separation Theorems: 26. Souslin¿Luzin separation theorem; 27. Kleen separation theorem; 28. ¿11 -reduction; 29. ¿11 -codes; Part IV. Gandy Forcing: 30. ¿11 equivalence relations; 31. Borel metric spaces and lines in the plane; 32. ¿11 equivalence relations; 33. Louveau's theorem; 34. Proof of Louveau's theorem; References; Index; Elephant sandwiches.
