Characterising one-player positionality for infinite duration games on graphs

I will present a new result, asserting that a winning condition (or, more generally, a valuation) which admits a neutral letter is positional over arbitrary arenas if and only if for all cardinals there exists a universal graph which is monotone and well-founded. Here, "positional" refers only to the protagonist; this concept is sometimes also called "half-positionality". This is the first known characterization in this setting. I will explain the result, quickly survey existing related work, show how it is proved and try to argue why it is interesting.