On a relation between $λ$-full well-ordered sets and weakly compact cardinals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916173323436032 |
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| author | Gullà, Gabriele |
| author_facet | Gullà, Gabriele |
| contents | We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $λ$, of a particular kind of well-ordered subsets characterized by the property of $λ$-fullness. Let $H$ be a set of regular cardinals: by using our results about well-ordered $λ$-full sets we show that if $\inf H$ is a weakly compact cardinal, then, for every LOTS $X$, $H$-compactness is equivalent to the nonexistence of gaps of types in $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a relation between $λ$-full well-ordered sets and weakly compact cardinals Gullà, Gabriele Logic General Topology We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $λ$, of a particular kind of well-ordered subsets characterized by the property of $λ$-fullness. Let $H$ be a set of regular cardinals: by using our results about well-ordered $λ$-full sets we show that if $\inf H$ is a weakly compact cardinal, then, for every LOTS $X$, $H$-compactness is equivalent to the nonexistence of gaps of types in $H$. |
| title | On a relation between $λ$-full well-ordered sets and weakly compact cardinals |
| topic | Logic General Topology |
| url | https://arxiv.org/abs/2403.15904 |