Δ03-determinacy, comprehension and induction
MedYahya Ould MedSalem and Kazuyuki Tanaka
Source: J. Symbolic Logic Volume 72, Issue 2
(2007), 452-462.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1185803618
Digital Object Identifier: doi:10.2178/jsl/1185803618
Mathematical Reviews number (MathSciNet): MR2320285
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