A note on the theory of positive induction, {{\rm ID}^*_1} |
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Authors: | Bahareh Afshari Michael Rathjen |
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Institution: | (1) Hines Hospital, VA Medical Center, Hines, IL, USA;(2) Northwestern University, 680 N. Lakeshore Drive, Suite 1220 Chicago, IL 60611, USA;(3) University of Illinois, Chicago, IL, USA |
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Abstract: | 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. |
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