On sharply bounded length induction
We construct models of the theory L 2 0 : = BASIC + Σ 0 b -LIND: one where the predecessor function is not total and one not satisfying Σ 0 2 -PIND, showing that L 2 0 is strictly weaker that S 2 0 . The construction also shows that S 2 0 is not ∀∑ 0 b -axiomatizable.
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