 For, by definition (*) is true in a model \(M\) iff the second-order sentence \((\exists f)(\exists g)(\forall x)(\forall z) R(x, f(x), z, g(z))\) is true therein. The latter may be termed the Skolem normal form of (*). It says that Skolem functions providing witnesses for the quantifiers \(\exists y\) and \(\exists w\) in (*) exist. Finite partially ordered quantifiers – a.k.a. Henkin quantifiers or branching quantifiers – were proposed by Leon Henkin (1961) and have been subsequently studied  extensively.[8]  They are two-dimensional syntactic objects