The computability problem is due to the unbounded ability of P to reason about theorems in the base theory (so that would be a necessary point of relaxation). A computable total function can’t even assign values > 1⁄2 to all the theorems of PA and values < 1⁄2 to all the sentences refuted by PA.
The computability problem is due to the unbounded ability of P to reason about theorems in the base theory (so that would be a necessary point of relaxation). A computable total function can’t even assign values > 1⁄2 to all the theorems of PA and values < 1⁄2 to all the sentences refuted by PA.