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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02297 |
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| _version_ | 1866912122288472064 |
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| author | Srivastava, Suyash Mittal, Mihir |
| author_facet | Srivastava, Suyash Mittal, Mihir |
| contents | The shuffle of a non-empty countable set $ S $ of linear orders is the (unique up to isomorphism) linear order $ Ξ(S) $ obtained by fixing a coloring function $ χ: \mathbb{Q} \to S $ having fibers dense in $ \mathbb{Q} $ and replacing each rational $ q $ in $ (\mathbb{Q}, <) $ with an isomorphic copy of $ χ(q) $. We prove that any two countable shuffles that embed as convex subsets into each other are order isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cantor-Schröder-Bernstein theorem for a class of countable linear orders Srivastava, Suyash Mittal, Mihir Logic Combinatorics 06A05 The shuffle of a non-empty countable set $ S $ of linear orders is the (unique up to isomorphism) linear order $ Ξ(S) $ obtained by fixing a coloring function $ χ: \mathbb{Q} \to S $ having fibers dense in $ \mathbb{Q} $ and replacing each rational $ q $ in $ (\mathbb{Q}, <) $ with an isomorphic copy of $ χ(q) $. We prove that any two countable shuffles that embed as convex subsets into each other are order isomorphic. |
| title | Cantor-Schröder-Bernstein theorem for a class of countable linear orders |
| topic | Logic Combinatorics 06A05 |
| url | https://arxiv.org/abs/2411.02297 |