Foundations with Imagination

Toby Meadows

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arXiv · 2601.20057

Foundations with Imagination

Toby Meadows

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Abstract

We show that countable set theory, $ZFC^{-}+\forall x\ |x|\leq\omega$, is unable to eliminate imaginaries. In other words, this theory cannot provide representatives for arbitrary definable equivalence relations. We also see that $ZFC^{-}$ and ZFC^{-}+\exists\kappa(Inacc(\kappa)\wedge\forall x\ |x|\leq\kappa)$ also fail to eliminate imaginaries.

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Toby Meadows. 2026-01-27. Foundations with Imagination. https://arxiv.org/abs/2601.20057

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