Some questions on entangled linear orders
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915946568876032 |
|---|---|
| author | Carroy, Raphaël Levine, Maxwell Notaro, Lorenzo |
| author_facet | Carroy, Raphaël Levine, Maxwell Notaro, Lorenzo |
| contents | Entangled linear orders were first introduced by Abraham and Shelah. Todorčević showed that these linear orders exist under $\mathsf{CH}$. We prove the following results: (1) If $\mathsf{CH}$ holds, then, for every $n > 0$, there is an $n$-entangled linear order which is not $(n+1)$-entangled. (2) If $\mathsf{CH}$ holds, then there are two homeomorphic sets of reals $A, B \subseteq \mathbb{R}$ such that $A$ is entangled but $B$ is not $2$-entangled. (3) If $\mathbb{R}\subseteq \mathrm{L}$, then there is an entangled $Π_1^1$ set of reals. (4) If $\diamondsuit$ holds, then there is a $2$-entangled non-separable linear order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some questions on entangled linear orders Carroy, Raphaël Levine, Maxwell Notaro, Lorenzo Logic Combinatorics 03E05 (Primary) 03E50, 03E15, 06A05 (Secondary) Entangled linear orders were first introduced by Abraham and Shelah. Todorčević showed that these linear orders exist under $\mathsf{CH}$. We prove the following results: (1) If $\mathsf{CH}$ holds, then, for every $n > 0$, there is an $n$-entangled linear order which is not $(n+1)$-entangled. (2) If $\mathsf{CH}$ holds, then there are two homeomorphic sets of reals $A, B \subseteq \mathbb{R}$ such that $A$ is entangled but $B$ is not $2$-entangled. (3) If $\mathbb{R}\subseteq \mathrm{L}$, then there is an entangled $Π_1^1$ set of reals. (4) If $\diamondsuit$ holds, then there is a $2$-entangled non-separable linear order. |
| title | Some questions on entangled linear orders |
| topic | Logic Combinatorics 03E05 (Primary) 03E50, 03E15, 06A05 (Secondary) |
| url | https://arxiv.org/abs/2507.17503 |