Weak well orders and Fraïssé's conjecture

Anton Freund; Davide Manca

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arXiv · 2304.03021

Weak well orders and Fraïssé's conjecture

Anton Freund·Davide Manca

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Abstract

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 Fraïssé's conjecture, which has been proved by Laver. We also fill a small gap in Shore's proof that Fraïssé's conjecture implies arithmetic transfinite recursion over ${\bf RCA}_0$, by giving a new proof of $Σ^0_2$-induction.

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Anton Freund, Davide Manca. 2023-04-06. Weak well orders and Fraïssé's conjecture. https://arxiv.org/abs/2304.03021

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