Descriptive Set Theory and Forcing - Miller, Arnold W.

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Résumé :
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis....

Biographie:
Arnold W. Miller works in the Department of Mathematics at the University of Wisconsin, Madison.

Sommaire:
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.