When thinking about the course “birational geometry for number theorists” I so näıvely agreed to give at the Göttingen summer school, I could not avoid imagining the spirit of the late Serge Lang, not so quietly beseeching one to do things right, keeping the theorems functorial with respect to ideas, and definitions natural. But most important is the fundamental tenet of Diophantine geometry, f...

After World War II, the Dutch architect Aldo van Eyck developed hundreds of playgrounds in the city of Amsterdam. These public playgrounds were located in parks, squares, and derelict sites, and consisted of minimalistic aesthetic play equipment that was supposed to stimulate the creativity of children. Over the last decades, these playgrounds have been studied by sociologists, theorists of art...

Game Logic (GL), introduced in [18], is examined from a game-theoretic perspective. A new semantics for GL is proposed in terms of untyped games which are closely related to extensive game forms of perfect information. An example is given of how GL can be used as a formal model of game situations, and some metatheoretic results are presented in the context of their game-theoretic relevance. 200...