Cardinal invariants of idealized Miller null sets
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918283719999488 |
|---|---|
| author | Cieślak, Aleksander Gappo, Takehiko Martínez-Celis, Arturo Yamazoe, Takashi |
| author_facet | Cieślak, Aleksander Gappo, Takehiko Martínez-Celis, Arturo Yamazoe, Takashi |
| contents | This paper provides an extensive study of the $\mathscr{I}$-Miller null ideals $M_\mathscr{I}$, $σ$-ideals on the Baire space parametrized by ideals $\mathscr{I}$ on countable sets. These $σ$-ideals are associated to the idealized versions of Miller forcing in the same way that the meager ideal is associated to Cohen forcing. We compute the cardinal invariants of $M_\mathscr{I}$ for typical examples of Borel ideals $\mathscr{I}$ and show that Cichoń's Maximum can be extended by adding the uniformity and covering numbers of $M_\mathscr{I}$ for different ideals $\mathscr{I}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cardinal invariants of idealized Miller null sets Cieślak, Aleksander Gappo, Takehiko Martínez-Celis, Arturo Yamazoe, Takashi Logic 03E05, 03E17, 03E35 This paper provides an extensive study of the $\mathscr{I}$-Miller null ideals $M_\mathscr{I}$, $σ$-ideals on the Baire space parametrized by ideals $\mathscr{I}$ on countable sets. These $σ$-ideals are associated to the idealized versions of Miller forcing in the same way that the meager ideal is associated to Cohen forcing. We compute the cardinal invariants of $M_\mathscr{I}$ for typical examples of Borel ideals $\mathscr{I}$ and show that Cichoń's Maximum can be extended by adding the uniformity and covering numbers of $M_\mathscr{I}$ for different ideals $\mathscr{I}$. |
| title | Cardinal invariants of idealized Miller null sets |
| topic | Logic 03E05, 03E17, 03E35 |
| url | https://arxiv.org/abs/2601.07428 |