弱井阶和fraÏssÉ的猜想

Pub Date : 2023-09-27 DOI:10.1017/jsl.2023.70

ANTON FREUND, DAVIDE MANCA

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引用次数: 0

摘要

可数井阶的概念允许在初始段之间的嵌入方面有另一种定义。我们用逆向数学的框架来研究这个定义的逻辑强度及其与Fraïssé猜想的联系，该猜想已被Laver证明。我们还通过给出$\Sigma ^0_2$ -归纳法的新证明，填补了Shore关于Fraïssé猜想在$\mathbf {RCA}_0$上蕴涵算术超限递归的证明中的一个小空白。

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WEAK WELL ORDERS AND FRAÏSSÉ’S CONJECTURE

Abstract The notion of countable 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 $\mathbf {RCA}_0$ , by giving a new proof of $\Sigma ^0_2$ -induction.

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