RELATIVE LEFTMOST PATH PRINCIPLES AND OMEGA-MODEL REFLECTIONS OF TRANSFINITE INDUCTIONS
YUDAI SUZUKI · Journal of Symbolic Logic · 2025
Abstract In this article, 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 $\Sigma ^0_{n}\mathsf {LPP}$ .