Remarks on Halin's end-degree Conjecture
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909958043336704 |
|---|---|
| author | Fernandes, Gabriel |
| author_facet | Fernandes, Gabriel |
| contents | We prove new instances of Halin's end degree conjecture (HC) in ZFC. In particular, we show that there is a proper class of cardinals kappa for which Halin's conjecture holds, answering two questions posed by Geschke, Kurkofka, Melcher, and Pitz (2023). We also investigate the relationship between HC and the Singular Cardinal Hypothesis, deriving consistency strength from failures of the former. Moreover, we verify that Halin's conjecture fails on finite intervals of successors of singular cardinals in Merimovich's model, yielding a new independence result concerning HC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on Halin's end-degree Conjecture Fernandes, Gabriel Logic Combinatorics 05C63, 03E05, 03E35 We prove new instances of Halin's end degree conjecture (HC) in ZFC. In particular, we show that there is a proper class of cardinals kappa for which Halin's conjecture holds, answering two questions posed by Geschke, Kurkofka, Melcher, and Pitz (2023). We also investigate the relationship between HC and the Singular Cardinal Hypothesis, deriving consistency strength from failures of the former. Moreover, we verify that Halin's conjecture fails on finite intervals of successors of singular cardinals in Merimovich's model, yielding a new independence result concerning HC. |
| title | Remarks on Halin's end-degree Conjecture |
| topic | Logic Combinatorics 05C63, 03E05, 03E35 |
| url | https://arxiv.org/abs/2411.11841 |