Direct reference to polynomial rates of growth is also avoided in the formulation of the first-order arithmetical theory now known as \(\text{I}\Delta_0\) (which was originally introduced by Parikh (1971) under the name \(\textsf{PB}\)). \(\text{I}\Delta_0\) is formulated over the traditional language of first-order arithmetic – i.e. \(\mathcal{L}_a = \{0,s,+,x,\lt\}\) – and consists of the axioms of Robinson’s \(\mathsf{Q}\) together with the restriction of the induction scheme of \(\mathsf{PA}\) arithmetic to \(\Delta_0\)-formulas – i.e. those containing only bounded quantifiers of the form \(\forall x \leq t\) or \(\exists x \leq t\) where \(t\) is a term not containing \(x\).