Mad families of vector subspaces and the smallest nonmeager set of reals
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909261798309888 |
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| author | Smythe, Iian B. |
| author_facet | Smythe, Iian B. |
| contents | We show that a parametrized $\diamondsuit$ principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoint family of block subspaces in a countable vector space is $\aleph_1$. Consequently, this cardinal invariant is $\aleph_1$ in the Miller model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_08078 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Mad families of vector subspaces and the smallest nonmeager set of reals Smythe, Iian B. Logic 03E17 (primary), 15A03 (secondary) We show that a parametrized $\diamondsuit$ principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoint family of block subspaces in a countable vector space is $\aleph_1$. Consequently, this cardinal invariant is $\aleph_1$ in the Miller model. |
| title | Mad families of vector subspaces and the smallest nonmeager set of reals |
| topic | Logic 03E17 (primary), 15A03 (secondary) |
| url | https://arxiv.org/abs/1909.08078 |