Henkin quantifiers: logic, games, and computation Merlijn Sevenster Abstract: In this paper, we study the game-theoretic and computational repercussions of Henkins partially ordered quantifiers. After defining a gametheoretic semantics for these objects, we observe that tuning the parameter of absentmindedness gives rise to quantifier prefixes studied. In the interest of computation, we characterize the complexity class P_{||}^{NP} in terms of partially ordered quantifiers, by means of a proof different from Gottlob's. We conclude with some research questions at the interface of logic, game theory, and complexity theory. Keywords: Henkin quantifier; game-theoretic semantics; descriptive complexity