feferman (2006) cites väänänen's 2001 result to argue (contra hintikka) that while satisfiability might be a first-order matter, the question of whether there is a winning strategy for verifier over all structures in general "lands us squarely in "full second order logic"" (emphasis feferman's). feferman also attacked the claimed usefulness of the extended if logic, because the sentences in formula_428 do not admit a game-theoretic interpretation.