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Dominique Lecomte, Université Paris 6, France
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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

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.

• 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