A lightface analysis of the differentiability rank

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Abstract

We examine the computable part of the differentiability hierarchy defined by Kechris and Woodin. In that hierarchy, the rank of a differentiable function is an ordinal less than  w1 which measures how complex it is to verify differentiability for that function.We show that for each recursive ordinalα > 0, the set of Turing indices of C[0, 1] functions that are differentiable with rank at most α is Π2α+1-complete. This result is expressed in the notation of Ash and Knight.

Original languageEnglish (US)
Pages (from-to)240-265
Number of pages26
JournalJournal of Symbolic Logic
Volume79
Issue number1
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Philosophy
  • Logic

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