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Author:   Arnold W. Miller (University of Wisconsin, Madison)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   4
Dimensions:   Width: 16.00cm , Height: 1.50cm , Length: 23.70cm
Weight:   0.360kg
ISBN:  

9781107168060

ISBN 10:   1107168066
Pages:   134
Publication Date:   18 May 2017
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

Reviews

'Miller includes interesting historical material and references. His taste for slick, elegant proofs makes the book pleasant to read. The author makes good use of his sense of humor ... Most readers will enjoy the comments, footnotes, and jokes scattered throughout the book.' Studia Logica

Author Information

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

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