**Memoirs of the American Mathematical Society**

2013;
83 pp;
Softcover

MSC: Primary 03;
Secondary 54; 28; 26

Print ISBN: 978-0-8218-7557-5

Product Code: MEMO/221/1038

List Price: $62.00

Individual Member Price: $37.20

**Electronic ISBN: 978-0-8218-9459-0
Product Code: MEMO/221/1038.E**

List Price: $62.00

Individual Member Price: $37.20

# Potential Wadge Classes

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*Dominique Lecomte*

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

# Table of Contents

## Potential Wadge Classes

- Chapter 1. Introduction 18 free
- Chapter 2. A condition ensuring the existence of complicated sets 714 free
- Chapter 3. The proof of Theorem 1.10 for the Borel classes 1320
- Chapter 4. The proof of Theorem 1.11 for the Borel classes 1724
- Chapter 5. The proof of Theorem 1.10 3340
- Chapter 6. The proof of Theorem 1.11 4754
- Chapter 7. Injectivity complements 7582
- Bibliography 8390