Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.00205 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929656171593728 |
|---|---|
| author | Kwela, Adam |
| author_facet | Kwela, Adam |
| contents | We study Egorov ideals, that is ideals on $ω$ for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{Σ^0_2}$ ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological $\bf{Σ^0_2}$ Egorov ideals. On the other hand, we construct $2^ω$ pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00205 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Egorov ideals Kwela, Adam Logic We study Egorov ideals, that is ideals on $ω$ for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological $\bf{Σ^0_2}$ ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological $\bf{Σ^0_2}$ Egorov ideals. On the other hand, we construct $2^ω$ pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov. |
| title | Egorov ideals |
| topic | Logic |
| url | https://arxiv.org/abs/2312.00205 |