Predicative collapsing principles

Journal of Symbolic Logic 85 (1):511-530 (2020)
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Abstract

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

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Bachmann–Howard derivatives.Anton Freund - 2023 - Archive for Mathematical Logic 62 (5):581-618.

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