PreprintCC BY 4.0HAL
The weakness of typicality
Abstract
Many statements studied in reverse mathematics can be seen as mathematical problems, formulated in terms of instances and solutions. We develop a framework of typicality encompassing measure and genericity, and we classify the reverse mathematics zoo in terms of which problems admit typical solutions. It turns out that even very weak problems do not admit typical solutions.
Related
BibTeX
@misc{astor2026weakness,
title = {{The weakness of typicality}},
author = {Eric P. Astor and Laurent Bienvenu and Damir D Dzhafarov and Ludovic Patey and Paul Shafer and Reed D Solomon and Linda Brown Westrick},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00884},
eprint = {2609.00884},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05820542v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The weakness of typicality
AU - Eric P. Astor
AU - Laurent Bienvenu
AU - Damir D Dzhafarov
AU - Ludovic Patey
AU - Paul Shafer
AU - Reed D Solomon
AU - Linda Brown Westrick
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.00884
UR - https://hal.science/hal-05820542v1
AB - Many statements studied in reverse mathematics can be seen as mathematical problems, formulated in terms of instances and solutions. We develop a framework of typicality encompassing measure and genericity, and we classify the reverse mathematics zoo in terms of which problems admit typical solutions. It turns out that even very weak problems do not admit typical solutions.
ER -