We look at diagonalization properties for sequences of various flavors of uniform covers of separable metric spaces and we describe them with game-theoretic and Ramsey-like partition properties. Applications include strong measure zero, null-additive and meager-additive sets in Polish groups, Menger-bounded spaces etc.
Some highlights: a link to fractal measures and how it can help with calculation of cardinal invariants; Galvin-Mycielski-Solovay Theorem in various contexts;a solution to a Scheepers problem regarding products of strong measure zero spaces.