Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911586674802688 |
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| author | Mihara, Tomoki |
| author_facet | Mihara, Tomoki |
| contents | Let $k$ be a complete valuation field. We formulate a free Banach $k$-vector space as a Banach $k$-vector space with an orthonormal Schauder basis, and an almost free Banach $k$-vector space as a non-Archimedean analogue of an almost free Abelian group. As non-Archimedean analogues of the classical facts that an almost free Abelian group is free under the assumption of the $\aleph_1$-strong compactness or the weak compactness of the cardinality, we show that an almost free Banach $k$-vector space is free under similar assumptions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals Mihara, Tomoki Logic Number Theory Let $k$ be a complete valuation field. We formulate a free Banach $k$-vector space as a Banach $k$-vector space with an orthonormal Schauder basis, and an almost free Banach $k$-vector space as a non-Archimedean analogue of an almost free Abelian group. As non-Archimedean analogues of the classical facts that an almost free Abelian group is free under the assumption of the $\aleph_1$-strong compactness or the weak compactness of the cardinality, we show that an almost free Banach $k$-vector space is free under similar assumptions. |
| title | Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals |
| topic | Logic Number Theory |
| url | https://arxiv.org/abs/2604.10526 |