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

The article shows a simple way of calibrating the strength of the theory of positive induction, ID^*₁{{\rm ID}^{*}_{1}} . Crucially the proof exploits the equivalence of S¹₁{\Sigma^{1}_{1}} dependent choice and ω-model reflection for P¹₂{\Pi^{1}_{2}} formulae over ACA ₀. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ID^*₁{{\rm ID}^{*}_{1}} in Probst, J Symb Log, 71, 721–746, 2006.