The Gluing Property
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866918409857400832 |
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| author | Hayut, Yair Poveda, Alejandro |
| author_facet | Hayut, Yair Poveda, Alejandro |
| contents | We introduce a new compactness principle which we call the gluing property. For a measurable cardinal $κ$ and a cardinal $λ$, we say that $κ$ has the $λ$-gluing property if every sequence of $λ$-many $κ$-complete ultrafilters on $κ$ can be glued into a $κ$-complete extender. We show that every $κ$-compact cardinal has the $2^κ$-gluing property, yet non-necessarily the $(2^κ)^+$-gluing property. Finally, we compute the exact consistency-strength for $κ$ to have the $ω$-gluing property; this being $o(κ)=ω_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03333 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Gluing Property Hayut, Yair Poveda, Alejandro Logic We introduce a new compactness principle which we call the gluing property. For a measurable cardinal $κ$ and a cardinal $λ$, we say that $κ$ has the $λ$-gluing property if every sequence of $λ$-many $κ$-complete ultrafilters on $κ$ can be glued into a $κ$-complete extender. We show that every $κ$-compact cardinal has the $2^κ$-gluing property, yet non-necessarily the $(2^κ)^+$-gluing property. Finally, we compute the exact consistency-strength for $κ$ to have the $ω$-gluing property; this being $o(κ)=ω_1$. |
| title | The Gluing Property |
| topic | Logic |
| url | https://arxiv.org/abs/2212.03333 |