Reflection Principles in ZFU
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917294292074496 |
|---|---|
| author | Glazer, Elliot Yao, Bokai |
| author_facet | Glazer, Elliot Yao, Bokai |
| contents | We separate the Collection Principle, the Reflection Principle, and the Partial Reflection Principle in ZF with urelements (ZFU), despite their equivalence under the Axiom of Choice. In particular, Collection and the Partial Reflection Principle are independent of one another, and Collection together with Partial Reflection does not imply the Reflection Principle. We show that Reflection and Collection are equivalent assuming either the Tail axiom or Small Violations of Choice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21970 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reflection Principles in ZFU Glazer, Elliot Yao, Bokai Logic We separate the Collection Principle, the Reflection Principle, and the Partial Reflection Principle in ZF with urelements (ZFU), despite their equivalence under the Axiom of Choice. In particular, Collection and the Partial Reflection Principle are independent of one another, and Collection together with Partial Reflection does not imply the Reflection Principle. We show that Reflection and Collection are equivalent assuming either the Tail axiom or Small Violations of Choice. |
| title | Reflection Principles in ZFU |
| topic | Logic |
| url | https://arxiv.org/abs/2602.21970 |