Recursion theory on weak fragments of Peano arithmetic: A study of definable cuts (Q2784778)

The paper gives a survey of recursion theory on weak fragments of Peano arithmetic PA. In particular the recursion theory under the hypothesis of \(B \Sigma_{1}\) is considered and results which are provably equivalent to \(I \Sigma_{1}\) over this basis theory are discussed. Further the recursion theory under \(B \Sigma_{2}\) is studied. The paper contains also some open problems.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00012].