PreprintCC BY-NC-ND 4.0arXiv
Ampleness in the Farey graph
Abstract
We show that the first-order theory of the Farey graph is $1$-ample but not $2$-ample. Along the way, we prove that it weakly eliminates imaginaries and observe that forking is trivial.
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BibTeX
@misc{khangheshlaghi2026ampleness,
title = {{Ampleness in the Farey graph}},
author = {Zahra Mohammadi Khangheshlaghi and Rizos Sklinos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02427},
eprint = {2609.02427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02427},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Ampleness in the Farey graph
AU - Zahra Mohammadi Khangheshlaghi
AU - Rizos Sklinos
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02427
UR - https://arxiv.org/abs/2609.02427
AB - We show that the first-order theory of the Farey graph is $1$-ample but not $2$-ample. Along the way, we prove that it weakly eliminates imaginaries and observe that forking is trivial.
ER -