Finite model theory for partially ordered connectives Merlijn Sevenster, Tero Tulenheimo Abstract: In the present article a study of the finite model theory of Henkin quantifiers with boolean variables, a.k.a. partially ordered connectives, is undertaken. The logic of first-order formulae prefixed by partially ordered connectives, denoted D, is considered on finite structures. D is characterized as a fragment of second-order existential logic \Sigma^1_1; the formulae of the relevant fragment do not allow existentially quantified variables as arguments of predicate variables. Using this characterization result, D is shown to harbor a strict hierarchy induced by the arity of predicate variables. Further, D is shown to capture NP over linearly ordered structures, and not to be closed under complementation. We conclude with a comparison between the logics D and \Sigma^1_1 on several metatheoretical properties. Keywords: descriptive complexity, computational complexity, partially ordered quantification