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

Author(s) Arnold W. Miller

Lecture Notes Logic, 4: 130pp. (1995).

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Lecture Notes in Logic, Volume 4

130 pp.

Published: 1995

First available in Project Euclid: 23 February 2009

MathSciNet: MR1439251

ISBN: 3540600590

Subjects:

Primary: 03E15 , 03E35

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Association for Symbolic Logic

TABLE OF CONTENTS
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Miscellaneous Frontmatter

Arnold W. Miller

Lecture Notes in Logic Vol. 4, - (1995). Open Access

Chapter 1: What are the reals, anyway?

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 5-6 (1995). Open Access

I: On the length of Borel hierarchies

Chapter 2: Borel Hierarchy

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 7-10 (1995). Open Access

Chapter 3: Abstract Borel hierarchies

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 11-12 (1995). Open Access

Chapter 4: Characteristic function of a sequence

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 13-15 (1995). Open Access

Chapter 5: Martin's Axiom

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 16-17 (1995). Open Access

Chapter 6: Generic $\emph{G}_{\delta}$

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 18-20 (1995). Open Access

Chapter 7: $\alpha$-forcing

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 21-25 (1995). Open Access

Chapter 8: Boolean algebras

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 26-29 (1995). Open Access

Chapter 9: Borel order of a field of sets

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 30-31 (1995). Open Access

Chapter 10: CH and orders of separable metric spaces

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 32-33 (1995). Open Access

Chapter 11: Martin-Solovay Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 34-37 (1995). Open Access

Chapter 12: Boolean algebra of order $\omega_1$

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 38-41 (1995). Open Access

Chapter 13: Luzin sets

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 42-45 (1995). Open Access

Chapter 14: Cohen real model

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 46-56 (1995). Open Access

Chapter 15: The random real model

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 57-63 (1995). Open Access

Chapter 16: Covering number of an ideal

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 64-67 (1995). Open Access

II: Analytic sets

Chapter 17: Analytic sets

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 68-70 (1995). Open Access

Chapter 18: Constructible well-orderings

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 71-71 (1995). Open Access

Chapter 19: Hereditarily countable sets

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 72-73 (1995). Open Access

Chapter 20: Shoenfield Absoluteness

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 74-75 (1995). Open Access

Chapter 21: Mansfield-Solovay Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 76-77 (1995). Open Access

Chapter 22: Uniformity and Scales

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 78-81 (1995). Open Access

Chapter 23: Martin's axiom and Constructibility

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 82-83 (1995). Open Access

Chapter 24: $\Sigma^1_2$ well-orderings

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 84-84 (1995). Open Access

Chapter 25: Large $\Pi^1_2$ sets

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 85-87 (1995). Open Access

III: Classical separation theorems

Chapter 26: Souslin-Luzin Separation Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 88-89 (1995). Open Access

Chapter 27: Kleene Separation Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 90-92 (1995). Open Access

Chapter 28: $\Pi^1_1$-Reduction

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 93-94 (1995). Open Access

Chapter 29: $\Delta^1_1$-codes

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 95-97 (1995). Open Access

IV: Gandy forcing

Chapter 30: $\Pi^1_1$ equivalence relations

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 98-102 (1995). Open Access

Chapter 31: Borel metric spaces and lines in the plane

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 103-106 (1995). Open Access

Chapter 32: $\Sigma^1_1$ equivalence relations

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 107-110 (1995). Open Access

Chapter 33: Louveau's Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 111-116 (1995). Open Access

Chapter 34: Proof of Louveau's Theorem

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 117-120 (1995). Open Access

References

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 121-127 (1995). Open Access

Index

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 128-129 (1995). Open Access

Elephant sandwiches

Arnold W. Miller

Lecture Notes in Logic Vol. 4, 130-130 (1995). Open Access

Miscellaneous Backmatter

Arnold W. Miller

Lecture Notes in Logic Vol. 4, - (1995). Open Access

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