Dense ideals
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929550066188288 |
|---|---|
| author | Eskew, Monroe Hayut, Yair |
| author_facet | Eskew, Monroe Hayut, Yair |
| contents | In this paper, we obtain the consistency, relative to large cardinals, of the existence of dense ideals on every successor of a regular cardinal simultaneously. Using a consequent transfer principle, we show that in this model there is a $σ$-complete, $\aleph_1$-dense ideal on $\aleph_{n+1}$ for every $n < ω$, answering a question of Foreman.
Using this construction we show the consistency of the existence of various irregular ultrafilters on $ω_n$, the consistency of the Foreman-Laver reflection property for the chromatic number of graphs for all possible pairs of cardinals below $\aleph_ω$, and the simultaneous consistency of the partition hypotheses $\mathrm{PH}_n(ω_m)$ for $n < m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dense ideals Eskew, Monroe Hayut, Yair Logic 03E55 In this paper, we obtain the consistency, relative to large cardinals, of the existence of dense ideals on every successor of a regular cardinal simultaneously. Using a consequent transfer principle, we show that in this model there is a $σ$-complete, $\aleph_1$-dense ideal on $\aleph_{n+1}$ for every $n < ω$, answering a question of Foreman. Using this construction we show the consistency of the existence of various irregular ultrafilters on $ω_n$, the consistency of the Foreman-Laver reflection property for the chromatic number of graphs for all possible pairs of cardinals below $\aleph_ω$, and the simultaneous consistency of the partition hypotheses $\mathrm{PH}_n(ω_m)$ for $n < m$. |
| title | Dense ideals |
| topic | Logic 03E55 |
| url | https://arxiv.org/abs/2410.14359 |