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Potential Wadge Classes
Dominique Lecomte, Université Paris 6, France

Memoirs of the American Mathematical Society
2013; 83 pp; softcover
Volume: 221
ISBN-10: 0-8218-7557-4
ISBN-13: 978-0-8218-7557-5
List Price: US$62
Individual Members: US$37.20
Institutional Members: US$49.60
Order Code: MEMO/221/1038
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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

  • Introduction
  • A condition ensuring the existence of complicated sets
  • The proof of Theorem 1.10 for the Borel classes
  • The proof of Theorem 1.11 for the Borel classes
  • The proof of Theorem 1.10
  • The proof of Theorem 1.11
  • Injectivity complements
  • Bibliography
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