Archive for Mathematical Logic

, Volume 49, Issue 2, pp 275–281 | Cite as

A note on the theory of positive induction, \({{\rm ID}^*_1}\)

  • Bahareh Afshari
  • Michael RathjenEmail author


The article shows a simple way of calibrating the strength of the theory of positive induction, \({{\rm ID}^{*}_{1}}\) . Crucially the proof exploits the equivalence of \({\Sigma^{1}_{1}}\) dependent choice and ω-model reflection for \({\Pi^{1}_{2}}\) formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of \({{\rm ID}^{*}_{1}}\) in Probst, J Symb Log, 71, 721–746, 2006.

Mathematics Subject Classification (2000)

03B30 03F25 03F35 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK

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