Slow reflection.

We describe a “slow” version of the hierarchy of uniform reflection principles over Peano Arithmetic ( PA ). These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce a new provably total function. At the same time the consistency of PA plus slow reflection is provable in PA + Con ( PA ) . We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely ε 0 stages between PA and PA + Con ( PA ) (where Con ( PA ) refers to the usual consistency statement). [ABSTRACT FROM AUTHOR]