Vector spaces with a union of independent subspaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909536418267136 |
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| author | Berarducci, Alessandro Mamino, Marcello Mennuni, Rosario |
| author_facet | Berarducci, Alessandro Mamino, Marcello Mennuni, Rosario |
| contents | Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and admits quantifier elimination in the language of $K$-vector spaces with predicates for the $n$-fold sums of $X$ with itself. If $K$ is finite this is no longer true, but we still have that a natural completion is near-model-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03867 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Vector spaces with a union of independent subspaces Berarducci, Alessandro Mamino, Marcello Mennuni, Rosario Logic Primary: 03C10. Secondary: 03C45, 03C60 Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and admits quantifier elimination in the language of $K$-vector spaces with predicates for the $n$-fold sums of $X$ with itself. If $K$ is finite this is no longer true, but we still have that a natural completion is near-model-complete. |
| title | Vector spaces with a union of independent subspaces |
| topic | Logic Primary: 03C10. Secondary: 03C45, 03C60 |
| url | https://arxiv.org/abs/2209.03867 |