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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.15644 |
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Table of 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.