Abstract:The recursion theoretic limit lemma, saying that each function with a $\varSigma _{n+2}$ graph is a limit of certain function with a $\varDelta _{n+1}$ graph, is provable in $\text {B}\Sigma _{n+1}$.
Keywords: limit lemma, fragments of arithmetic, collection scheme
AMS Subject Classification: 03F30, 03D55