Arnold W. Miller

Descriptive Set Theory and Forcing

• Gebundenes Buch

Produktbeschreibung

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 136
• Erscheinungstermin: 13. Februar 2017
• Englisch
• Abmessung: 235mm x 157mm x 12mm
• Gewicht: 361g
• ISBN-13: 9781107168060
• ISBN-10: 1107168066
• Artikelnr.: 46511881

Autorenporträt

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

Inhaltsangabe

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.