 Peano arithmetic \(\mathbf{PA}\) comes from Heyting arithmetic \(\mathbf{HA}\) by adding LEM or \(\neg \neg A \rightarrow A\) to the list of logical axioms, i.e., by using classical instead of intuitionistic logic. The following results hold even in the fragments of \(\mathbf{HA}\) and \(\mathbf{PA}\) with the induction schema restricted to \(\Delta_0\) formulas.