Descriptive set theory and forcing : how to prove theorems about Borel sets the hard way
著者
書誌事項
Descriptive set theory and forcing : how to prove theorems about Borel sets the hard way
（Lecture notes in logic, 4）
Springer-Verlag, c1995
- : gw
- : us
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible lengths of a Borel hierarchy in a separable metric space. The second half goes on to include Harrington's Theorem together with a proof and applications of Louveau's Theorem on hyperprojective parameters.
目次
1 What are the reals, anyway?.- 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-Solovay 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.- II Analytic sets.- 17 Analytic sets.- 18 Constructible well-orderings.- 19 Hereditarily countable sets.- 20 Shoenfield Absoluteness.- 21 Mansfield-Solovay Theorem.- 22 Uniformity and Scales.- 23 Martin's axiom and Constructibility.- 24
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$$-Reduction.- 29
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