Abstract
We show that each of Δ13-CA0 + Σ13-IND and Π12-CA0 + Π13-TI proves Δ03-Det and that neither Σ31-IND nor Π13-TI can be dropped. We also show that neither Δ13-CA0 + Σ1∞-IND nor Π12-CA0 + Π1∞-TI proves Σ03-Det. Moreover, we prove that none of Δ21-CA0, Σ31-IND and Π21-TI is provable in Δ11-Det0 = ACA0 + Δ11-Det.
Citation
MedYahya Ould MedSalem. Kazuyuki Tanaka. "Δ03-determinacy, comprehension and induction." J. Symbolic Logic 72 (2) 452 - 462, June 2007. https://doi.org/10.2178/jsl/1185803618
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