Structure and definability in general bounded arithmetic theories (Q1125060)

The paper is devoted to the study of bounded arithmetic theories. The main problems studied are motivated by the following questions: (1) What are the \(\Sigma^b_{i+1}\)-definable multifunctions of \(R^i_2\)? (2) When is one theory conservative over another? To answer these questions, versions of the theories \(R^i_2\), \(S^i_2\) and \(T^i_2\) with induction restricted to prenex formulas are introduced and studied.