 By a result of Hintikka (1955), the problem of deciding whether a sentence of second-order logic is valid can be effectively reduced to the validity problem of  \(\mathbf{IFL}\).[72]  Väänänen (2001) has shown that the set of valid sentences of \(\mathbf{IFL}\) has the same very high complexity as the set of validities of the full second-order  logic.[73]  Väänänen (2001) and Feferman (2006) conclude that speaking of validity in \(\mathbf{IFL}\) leads to a strong commitment to full second-order logic. Hintikka (2006a: 476–477) looks at these results from the opposite direction: for him they mean that indeed one can speak of validity in full second-order logic in terms of validity in \(\mathbf{IFL}\). What is more, Hintikka (1997) affirms that even \(\mathbf{EIFL}\) is a first-order logic. If so, any mathematical theory that can be expressed by the truth of an \(\mathbf{EIFL}\) sentence is likewise free from problems of set existence. 