Journal of Symbolic Logic

Δ03-determinacy, comprehension and induction

MedYahya Ould MedSalem and Kazuyuki Tanaka

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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.

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J. Symbolic Logic, Volume 72, Issue 2 (2007), 452-462.

First available in Project Euclid: 30 July 2007

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MedSalem, MedYahya Ould; Tanaka, Kazuyuki. Δ 0 3 -determinacy, comprehension and induction. J. Symbolic Logic 72 (2007), no. 2, 452--462. doi:10.2178/jsl/1185803618.

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