The strength of sharply bounded induction requires [formula omitted

Abstract

We show that the arithmetical theory T 2 0 + Σ ˆ 1 b - I N D ∣ x ∣ 5 , formalized in the language of Buss, i.e. with ⌊ x / 2 ⌋ but without the M S P function ⌊ x / 2 y ⌋ , does not prove that every nontrivial divisor of a power of 2 is even. It follows that this theory proves neither N P = c o N P nor S 2 0 .