Descriptive Set Theory and Forcing

Descriptive Set Theory and Forcing : How to prove theorems about Borel sets the hard way

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Description

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.
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Product details

  • Paperback | 133 pages
  • 155 x 235 x 7.62mm | 225g
  • Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Berlin, Germany
  • English
  • 1995 ed.
  • 1 Illustrations, black and white; IV, 133 p. 1 illus.
  • 3540600590
  • 9783540600596

Table of contents

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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Review Text

"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
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Review quote

"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
show more