Locally countable graphs of second projective class not generated by countably many projective functions
Logic
2026-05-26 v5
Abstract
To answer a question by Rettich and Serafin, we define a model of set theory in which there exists a locally countable graph on a subset of the real line, which is not generated by a countable family of projective (or even real-ordinal definable, ROD) functions. We also prove that the equi-constructibility graph on the reals is not generated by a countable family of ROD functions in the Solovay model.
Cite
@article{arxiv.2605.03126,
title = {Locally countable graphs of second projective class not generated by countably many projective functions},
author = {Vladimir Kanovei and Vassily Lyubetsky},
journal= {arXiv preprint arXiv:2605.03126},
year = {2026}
}