Abstract
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.
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Research of the second author was supported by a Royal Society International Joint Projects award 2006/R3.
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Afshari, B., Rathjen, M. A note on the theory of positive induction, \({{\rm ID}^*_1}\) . Arch. Math. Logic 49, 275–281 (2010). https://doi.org/10.1007/s00153-009-0168-9
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DOI: https://doi.org/10.1007/s00153-009-0168-9