Necessity of Σ¹₁ induction in Conidis’s reversals relating Σ¹₁AC, ABW, and SL

Ascertain whether Σ¹₁ induction is actually necessary to prove the equivalences and implications among Σ¹₁AC, ABW (arithmetic Bolzano–Weierstrass), and SL (sequential limit) over RCA, as claimed by Conidis, given that the published proofs appear to use Σ¹₁ induction explicitly.

Background

Conidis (2012) states that certain equivalences and implications among Σ¹₁AC, ABW, and SL can be proved over RCA without using Σ¹₁ induction. The present paper notes explicit uses of Σ¹₁IND in Conidis’s proofs and raises doubt about whether induction is avoidable.

Clarifying this point is important for accurately calibrating the strength of these theorems within reverse mathematics, specifically whether the induction scheme is essential for the reversals in question.