PreprintCC BY 4.0arXiv
1-genericity and almost everywhere domination
Abstract
We prove that there is a 1-generic set which computes a uniformly almost everywhere dominating function. The proof has two ingredients: a Baire space version of the Chong-Downey Sigma01-density criterion and the forcing of Cholak-Greenberg-Miller.
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BibTeX
@misc{zhao20261genericity,
title = {{1-genericity and almost everywhere domination}},
author = {Xuanheng Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18001},
eprint = {2609.18001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - 1-genericity and almost everywhere domination
AU - Xuanheng Zhao
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18001
UR - https://arxiv.org/abs/2609.18001
AB - We prove that there is a 1-generic set which computes a uniformly almost everywhere dominating function. The proof has two ingredients: a Baire space version of the Chong-Downey Sigma01-density criterion and the forcing of Cholak-Greenberg-Miller.
ER -