Weak well orders and Fraïssé's conjecture

Anton Freund, Davide Manca

Published 2023-04-06Version 1

The notion of well order admits an alternative definition in terms of embeddings between initial segments. We use the framework of reverse mathematics to investigate the logical strength of this definition and its connection with Fra\"iss\'e's conjecture, which has been proved by Laver. We also fill a small gap in Shore's proof that Fra\"iss\'e's conjecture implies arithmetic transfinite recursion over ${\bf RCA}_0$, by giving a new proof of $\Sigma^0_2$-induction.