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 ${\hat{I}}_{n+1}^1$ transfinite induction is equivalent to the $\hat{I}{\pounds }_n^0$ relative leftmost path principle over ${\mathsf{RCA}}_0$ for $n>1$. As a consequence, we have that $\hat{I}{\pounds }_{n+1}^0\mathsf{LPP}$ is strictly stronger than $\hat{I}{\pounds }_n^0\mathsf{LPP}$.

13 pages