We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal α there exists an ordinal β such that $1 + \beta \cdot \left( {\beta + \alpha } \right)$ (ordinal arithmetic) admits an almost order preserving collapse into β. Arithmetical comprehension is equivalent to a statement of the same form, with $\beta \cdot \alpha$ at the place of $\beta \cdot \left( {\beta + \alpha } \right)$. We will also characterize the principles that any set is contained in a countable coded ω-model of arithmetical transfinite recursion and arithmetical comprehension, respectively.

中文翻译：

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预测折叠原则

我们证明了算术超限递归等价于以下的适当形式化：对于每个序数α存在一个序数β这样$1 + \beta \cdot \left( {\beta + \alpha } \right)$（序数算术）承认一个几乎保持顺序的崩溃到β. 算术理解等价于相同形式的陈述，用$\beta \cdot \alpha$在的地方$\beta \cdot \left( {\beta + \alpha } \right)$. 我们还将描述任何集合都包含在可数编码中的原则ω-分别是算术超限递归和算术理解的模型。