On two theorems of positional games

I give fully detailed proofs of two important theorems—the exact solution of the weak clique game and the compactness theorem—in the theory of positional games. Both results were published several years ago, including an outline of the proofs that explained the basic idea, but left some technical details to the reader. Unfortunately, in both cases these details turned out to be highly non-trivial. Several mathematicians asked me for help; asked me to clarify the missing details. This is why I felt obliged to write this paper.