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arXiv · 1906.07448

Predicative collapsing principles

Anton Freund
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Abstract

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 $1+β\cdot(β+α)$ (ordinal arithmetic) admits an almost order preserving collapse into $β$. Arithmetical comprehension is equivalent to a statement of the same form, with $β\cdotα$ at the place of $β\cdot(β+α)$. We will also characterize the principles that any set is contained in a countable coded $ω$-model of arithmetical transfinite recursion resp. arithmetical comprehension.

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Anton Freund. 2020-08-05. Predicative collapsing principles. https://doi.org/10.1017/jsl.2019.83

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