Affiliations: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 University of Helsinki, Finland. juha.kontinen@helsinki.fi | Department of Mathematics and Statistics, University of Helsinki, Finland. ville.v.nurmi@gmail.com
Note: [] Supported by grant 127661 of the Academy of Finland and the European Science Foundation Eurocores programme LogICCC [FP002 - Logic for Interaction (LINT)] through grant 129208 of the Academy of Finland
Note: [] Supported by the MALJA Graduate school in Mathematical logic
Abstract: Team logic is a new logic, introduced by Väänänen [12], extending dependence logic by classical negation. Dependence logic adds to first-order logic atomic formulas expressing functional dependence of variables on each other. It is known that on the level of sentences dependence logic and team logic are equivalent with existential second-order logic and full second-order logic, respectively. In this article we show that, in a sense that we make explicit, team logic and second-order logic are also equivalent with respect to open formulas. A similar earlier result relating open formulas of dependence logic to the negative fragment of existential second-order logic was proved in [8].
