The Recursively Mahlo Property in Second Order Arithmetic
Michael Rathjen · Mathematical logic quarterly · 1996
Abstract The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof‐theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β‐model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional. Mathematics Subject Classification: 03F35, 03F15, 03E70.