Abstract
It is shown that the intuitionistic theory of polynomial induction on positive Π1b (coNP) formulas does not prove the sentence ¬¬∀x, yz ≤ y(x ≤ |y| → x = |z|). This implies the unprovability of the scheme ¬¬PIND(Σ1b+) in the mentioned theory. However, this theory contains the sentence ∀x, y¬¬z ≤ y(x ≤ |y| → x = |z|). The above independence result is proved by constructing an ω-chain of submodels of a countable model of S2 + Ω3 + ¬exp such that none of the worlds in the chain satisfies the sentence, and interpreting the chain as a Kripke model.
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