PreprintCC BY-NC-SA 4.0arXiv
Controlling The Skips of Arithmetic Sets
Abstract
Andrews, Ganchev, Kuyper, Lempp, Miller, A.\ Soskova, and M.\ Soskova conjectured that skip-cototality coincides with weak cototality. We show that the conjecture is false by constructing a Π02 set whose skip does not have a cototal degree. We further adapt this construction to obtain additional results. We prove that for each odd n, there is a Π0n+1 degree whose n-iterated skip does not have a cototal degree. We show that there is a Π02 degree which does not contain an introenumerable set.
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BibTeX
@misc{em2026controlling,
title = {{Controlling The Skips of Arithmetic Sets}},
author = {Taeyoung Em},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14399},
eprint = {2610.14399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14399},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Controlling The Skips of Arithmetic Sets
AU - Taeyoung Em
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14399
UR - https://arxiv.org/abs/2610.14399
AB - Andrews, Ganchev, Kuyper, Lempp, Miller, A.\ Soskova, and M.\ Soskova conjectured that skip-cototality coincides with weak cototality. We show that the conjecture is false by constructing a Π^0_2 set whose skip does not have a cototal degree. We further adapt this construction to obtain additional results. We prove that for each odd n, there is a Π^0_n+1 degree whose n-iterated skip does not have a cototal degree. We show that there is a Π^0_2 degree which does not contain an introenumerable set.
ER -