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

Abstract

In this paper, we give characterizations of Towsner's relative leftmost path principles in terms of omega-model reflections of transfinite inductions. In particular, we show that the omega-model reflection of $\Pi^1_{n+1}$ transfinite induction is equivalent to the $\Sigma^0_n$ relative leftmost path principle over $\mathsf{RCA}_0$ for $n > 1$. As a consequence, we have that $\Sigma^0_{n+1}\mathsf{LPP}$ is strictly stronger than $\Sigma^0_{n}\mathsf{LPP}$.