Set Theory of Infinite Imperfect Information Games Benedikt Löwe Abstract: We survey the recent developments in the investigation of Blackwell determinacy axioms. It is generally believed that ordinary (Gale-Stewart) determinacy and Blackwell determinacy for infinite games are equivalent in a strong sense, but this conjecture (of Tony Martin's) has not yet been proved. The paper is a snapshot of the current state-of-the-art knowledge in this area.