Relative leftmost path principles and omega-model reflections of transfinite inductions

In this paper, we show that the omega-model reflection of Π¹ₙ₊₁ transfinite induction is equivalent to Towsner's Σ⁰ₙ relative leftmost path principle Σ⁰ₙLPP over RCA₀ for $n > 1$. As a consequence, we have that Σ⁰ₙ₊₁LPP is strictly stronger than Σ⁰ₙLPP.