The theorists in this volume have confronted the exercise presented to them in vastly different ways. As editors, we asked them “to consider how you would evaluate this program” and “to make and specify assumptions about the program context.” The primary task, however, was to describe “a course of action, which may have consequences that lead to other evaluation design decisions.” All of the th...

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...

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...