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.

This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.

This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.

While recent studies have highlighted the phenomenon and risks of increased inequalities between the top and the bottom of society, little research has so far been carried out on trends relating to the median income range that generally represents the middle class. This volume examines the following questions: what are the main transformations in the world of work over the last 20 years in terms of the labour market, social dialogue, and conditions of work, wages and incomes that may have affected the middle class? How has the middle class been altered by the financial and economic crisis? What are the long-term trends for the middle class in Europe?

These proceedings present an overview of approaches for assessing subsidies and associated taxes and look at country experiences in reforming subsidies in agriculture, fisheries, industry and transport.