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, $${{\rm ID}^{*}_{1}}$$ . Crucially the proof exploits the equivalence of $${\Sigma^{1}_{1}}$$ dependent choice and ω-model reflection for $${\Pi^{1}_{2}}$$ formulae over ACA0. 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.