Descriptive set theory and forcing : how to prove theorems about borel sets the hard way / Arnold W. Miller.
These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets.
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Full Text (via Cambridge) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2017.
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| Series: | Lecture notes in logic ;
4. |
| Subjects: |
Table of Contents:
- I
- On the length of Borel hierarchies
- Borel Hierarchy
- Abstract Borel hierarchies
- Characteristic function of a sequence
- Martin's Axiom
- Generic G[textdelta]
- [textalpha]-forcing
- Boolean algebras
- Borel order of a field of sets
- CH and orders of separable metric spaces
- Martin-Solovay Theorem
- Boolean algebra of order [textomega]
- Luzin sets
- Cohen real model
- The random real model
- Covering number of an ideal
- II
- Analytic sets
- Analytic sets
- Constructible well-orderings
- Hereditarily countable sets
- Shoenfield Absoluteness
- Mansfield-Solovay Theorem
- Uniformity and Scales
- Martin's axiom and Constructibility
- well-orderings
- Large sets
- III
- Classical Separation Theorems
- Souslin-Luzin Separation Theorem
- Kleene Separation Theorem
- -Reduction
- -codes
- IV
- Gandy Forcing
- equivalence relations
- Borel metric spaces and lines in the plane
- equivalence relations
- Louveau's Theorem
- Proof of Louveau's Theorem.