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Well-ordering principles over recursive comprehension
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 RCA0, while previous results of Arai, Pakhomov-Walsh and Buriola-Weiermann required the stronger base theory ACA0. On the way, we strengthen a result of Carlucci-Mainardi-Rathjen about the ordinal analysis of theories of the form RCA0+``α$ is a well-order"}$.
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BibTeX
@misc{buriola2026wellordering,
title = {{Well-ordering principles over recursive comprehension}},
author = {Gabriele Buriola and Giacomo Cozzi and Antonia Dammrau and Anton Freund},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26336},
eprint = {2610.26336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26336},
}
RIS
TY - UNPB
TI - Well-ordering principles over recursive comprehension
AU - Gabriele Buriola
AU - Giacomo Cozzi
AU - Antonia Dammrau
AU - Anton Freund
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26336
UR - https://arxiv.org/abs/2610.26336
AB - We establish a general result on the proof-theoretic strength of well-ordering principles in reverse mathematics. The novelty is that our result gives information over base theories as weak as RCA_0, while previous results of Arai, Pakhomov-Walsh and Buriola-Weiermann required the stronger base theory ACA_0. On the way, we strengthen a result of Carlucci-Mainardi-Rathjen about the ordinal analysis of theories of the form RCA_0+``α$ is a well-order"}$.
ER -