Foundations with Imagination
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910003062898688 |
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| author | Meadows, Toby |
| author_facet | Meadows, Toby |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20057 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Foundations with Imagination Meadows, Toby Logic 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. |
| title | Foundations with Imagination |
| topic | Logic |
| url | https://arxiv.org/abs/2601.20057 |