Source: J. Symbolic Logic
Volume 72, Issue 2
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
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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