\(\Delta_ 0\)-complexity of the relation \(y= \prod_{i\leq n} F(i)\)
The authors prove that if \(G\) is a \(\Delta_0\)-definable function on the natural numbers and \(F(n)= \prod^n_{i=0} G(i)\), then \(F\) is also \(\Delta_0\)-definable. Moreover, the inductive properties of \(F\) can be proved inside that theory \(I\Delta_0\). The authors use the standard notation \(I\Delta_0\) to denote the fragment of Peano arithmetic where induction is restricted to bounded formulas (\(\Delta_0\)-formulas).
induction restricted to bounded formulas
scientific article; zbMATH DE number 802546
scientific article