Recall that a function \(f(\vec{x})\) is provably total in a theory \(\mathsf{T}\) just in case there is a \(\Sigma_1\)-formula \(\phi_f(\vec{x},y)\) defining the graph of \(f(\vec{x})\) in the language of \(\mathsf{T}\) such that \(\mathsf{T} \vdash \forall \vec{x} \exists ! y \phi_f(\vec{x},y)\). Since terms in the language of arithmetic are polynomials with positive coefficients, it follows from Theorem 4.3 that all of the provably total functions of \(\text{I}\Delta_0\) are of polynomial rate of growth. In particular, exponentiation is not provably total in this theory.  For this reason Parikh referred to \(\text{I}\Delta_0\) as an “anthropomorphic system”.[47]