Foundations with Imagination
Abstract
We show that countable set theory, $ZFC^{-}+\forall x\ |x|\leqω$, 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^{-}+\existsκ(Inacc(κ)\wedge\forall x\ |x|\leqκ)$ also fail to eliminate imaginaries.
Fields of Study & Subjects
Advanced Topology and Set Theory
Rings
Modules
and Algebras
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint