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Potential Wadge Classes
 
Dominique Lecomte Université Paris 6, Paris, France
Front Cover for Potential Wadge Classes
Available Formats:
Electronic ISBN: 978-0-8218-9459-0
Product Code: MEMO/221/1038.E
83 pp 
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
Front Cover for Potential Wadge Classes
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  • Front Cover for Potential Wadge Classes
  • Back Cover for Potential Wadge Classes
Potential Wadge Classes
Dominique Lecomte Université Paris 6, Paris, France
Available Formats:
Electronic ISBN:  978-0-8218-9459-0
Product Code:  MEMO/221/1038.E
83 pp 
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $37.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2212013
    MSC: Primary 03; Secondary 54; 28; 26;

    Let \(\bf\Gamma\) be a Borel class, or a Wadge class of Borel sets, and \(2\!\leq\! d\!\leq\!\omega\) be a cardinal. A Borel subset \(B\) of \({\mathbb R}^d\) is potentially in \(\bf\Gamma\) if there is a finer Polish topology on \(\mathbb R\) such that \(B\) is in \(\bf\Gamma\) when \({\mathbb R}^d\) is equipped with the new product topology. The author provides a way to recognize the sets potentially in \(\bf\Gamma\) and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. A condition ensuring the existence of complicated sets
    • 3. The proof of Theorem 1.10 for the Borel classes
    • 4. The proof of Theorem 1.11 for the Borel classes
    • 5. The proof of Theorem 1.10
    • 6. The proof of Theorem 1.11
    • 7. Injectivity complements
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Volume: 2212013
MSC: Primary 03; Secondary 54; 28; 26;

Let \(\bf\Gamma\) be a Borel class, or a Wadge class of Borel sets, and \(2\!\leq\! d\!\leq\!\omega\) be a cardinal. A Borel subset \(B\) of \({\mathbb R}^d\) is potentially in \(\bf\Gamma\) if there is a finer Polish topology on \(\mathbb R\) such that \(B\) is in \(\bf\Gamma\) when \({\mathbb R}^d\) is equipped with the new product topology. The author provides a way to recognize the sets potentially in \(\bf\Gamma\) and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.

  • Chapters
  • 1. Introduction
  • 2. A condition ensuring the existence of complicated sets
  • 3. The proof of Theorem 1.10 for the Borel classes
  • 4. The proof of Theorem 1.11 for the Borel classes
  • 5. The proof of Theorem 1.10
  • 6. The proof of Theorem 1.11
  • 7. Injectivity complements
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