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Abstract
We describe a "slow" version of the hierarchy of uniform reflection principles over Peano Arithmetic (). 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 plus slow reflection is provable in . We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely stages between and (where refers to the usual consistency statement).
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