Potential Wadge Classes (Memoirs of the American Mathematical Society)
Potential Wadge Classes (Memoirs of the American Mathematical Society) by Dominique Lecomte
English | 2013 | ISBN: 0821875574 | 83 Pages | PDF | 831.94 KB
English | 2013 | ISBN: 0821875574 | 83 Pages | PDF | 831.94 KB
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.