Foundations with Imagination
Logic
2026-01-29 v1
Abstract
We show that countable set theory, , is unable to eliminate imaginaries. In other words, this theory cannot provide representatives for arbitrary definable equivalence relations. We also see that and ZFC^{-}+\exists\kappa(Inacc(\kappa)\wedge\forall x\ |x|\leq\kappa)$ also fail to eliminate imaginaries.
Cite
@article{arxiv.2601.20057,
title = {Foundations with Imagination},
author = {Toby Meadows},
journal= {arXiv preprint arXiv:2601.20057},
year = {2026}
}