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In this paper, we show that the omega-model reflection of ¹₍+₁ transfinite induction is equivalent to Towsner's ⁰ₙ relative leftmost path principle ⁰ₙLPP over RCA₀ for n > 1. As a consequence, we have that ⁰₍+₁LPP is strictly stronger than ⁰₍LPP.
Yudai Suzuki (Thu,) studied this question.