Linear Orders and the Real Line
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915455700041728 |
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| author | Smith, Trey Ozer, Aksel |
| author_facet | Smith, Trey Ozer, Aksel |
| contents | Definitions of dense linear orders (with/without endpoints), separable linear orders, complete linear orders, the countable chain condition for linear orders, a Suslin line/Suslin tree and Suslin's problem Statement and proof of Cantor's Theorem characterizing (Q,<) as the only countable dense linear order without endpoints, up to isomorphism, the corollary which characterizes (R,<) as the only separable complete dense linear order without endpoints, every countable linear order embeds into (Q,<) (and thus, into (R,<)). Explanation of why Suslin lines and Suslin trees are equivalent, what an Aronszjan line/tree is, how it's a weakening of a Suslin line/tree. History and independence of Suslin's problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Orders and the Real Line Smith, Trey Ozer, Aksel Number Theory Definitions of dense linear orders (with/without endpoints), separable linear orders, complete linear orders, the countable chain condition for linear orders, a Suslin line/Suslin tree and Suslin's problem Statement and proof of Cantor's Theorem characterizing (Q,<) as the only countable dense linear order without endpoints, up to isomorphism, the corollary which characterizes (R,<) as the only separable complete dense linear order without endpoints, every countable linear order embeds into (Q,<) (and thus, into (R,<)). Explanation of why Suslin lines and Suslin trees are equivalent, what an Aronszjan line/tree is, how it's a weakening of a Suslin line/tree. History and independence of Suslin's problem. |
| title | Linear Orders and the Real Line |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.15644 |