 This definition of absoluteness is equivalent to the following more syntactic condition (Feferman &amp; Kreisel 1966): there are a \(\Sigma_1\)-formula \(\exists y\,\psi(y,x_1,\ldots,x_n)\) and a \(\Pi_1\)-formula \(\forall y\,\theta(y,x_1,\ldots,x_n)\) such that 