Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way (Lecture Notes...

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Arnold W. Miller

Descriptive Set Theory and Forcing

How to Prove Theorems about Borel Sets the Hard Way (Lecture Notes in Logic #4)

Arnold W. Miller

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English

Cambridge University Press
18 May 2017

Mathematical logic; Set theory; Topology

Series: Lecture Notes in Logic

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.

By: Arnold W. Miller
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 4
Dimensions: Height: 237mm, Width: 160mm, Spine: 15mm
Weight: 360g
ISBN: 9781107168060
ISBN 10: 1107168066
Series: Lecture Notes in Logic
Pages: 136
Publication Date: 18 May 2017
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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

Reviews for Descriptive Set Theory and Forcing: How to Prove Theorems about Borel Sets the Hard Way (Lecture Notes in Logic #4)

'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