Several set-theoretic principles about determinacy stronger than Borel determinacy are studied in descriptive set theory. The axiom of determinacy states that all subsets of all Polish spaces are determined. This is related to the fact that ZFC proves Borel determinacy, but not projective determinacy. Not all games require the axiom of determinacy to prove them determined. The axiom of determinacy is the statement that all such games are determined. The consistency of the existence of Woodin cardinals can be proved using determinacy hypotheses. As a corollary, he obtained a sufficient condition for the determinacy of the moment problem. Wadge determinacy implies the semilinear ordering principle for the Wadge order. This type of mount is designed according to the principles of kinematic determinacy. See reverse mathematics for other relations between determinacy and subsystems of second-order arithmetic. However, the determinacy of "infinite" games of imperfect information (Blackwell games) is less clear. He has made many notable contributions to the theory of inner models and determinacy. These requirements are, in no particular order&colon; Robustness, Determinacy, Compatibility. There is an intimate relationship between determinacy and large cardinals. Contemporary research in set theory includes the study of large cardinals and determinacy.