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- Title
PREDICATIVE COLLAPSING PRINCIPLES.
- Authors
FREUND, ANTON
- 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 $1 + \beta \cdot \left({\beta + \alpha } \right)$ (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.
- Subjects
COMPREHENSION; REVERSE mathematics
- Publication
Journal of Symbolic Logic, 2020, Vol 85, Issue 1, p511
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2019.83