Potential Wadge Classes
Author： Dominique Lecomte
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9780821894590
P-ISBN(Paperback): 9780821875575
P-ISBN(Hardback): 9780821875575
Subject： O144 Set Theory
Keyword： Logic and Foundations
Language： ENG
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Potential Wadge Classes
Description
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.