 for all formulae \({F}\in\cC\) in which X does not occur. Natural formula classes are the arithmetical formulae, consisting of all formulae without second order quantifiers \(\forall X\) and \(\exists X\), and the \(\Pi^1_n\)-formulae, where a \(\Pi^1_n\)-formula is a formula of the form \(\forall X_1\ldots Q X_n\,A(X_1,\ldots,X_n)\) with \(\forall X_1\ldots Q X_n\) being a string of n alternating set quantifiers, commencing with a universal one, followed by an arithmetical formula \(A(X_1,\ldots,X_n)\). Note that in this notation the class of arithmetical formulae is denoted by \(\Pi^1_0\).