Year: 2026
Type: preprint
Abstract: We establish a general result on the proof-theoretic strength of well-ordering principles in reverse mathematics. The novelty is that our result gives information over base theories as weak as $\mathsf{RCA}_0$, while previous results of Arai, Pakhomov-Walsh and Buriola-Weiermann required the stronger base theory $\mathsf{ACA}_0$. On the way, we strengthen a result of Carlucci-Mainardi-Rathjen about the ordinal analysis of theories of the form $\mathsf{RCA}_0+\text{``$α$ is a well-order"}$.
Source: arXiv (Cornell University)
Institution: University of Würzburg
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223040596