Distinguishing Martin's axiom from its restrictions
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909227211030528 |
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| author | Peng, Yinhe |
| author_facet | Peng, Yinhe |
| contents | We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions satisfying the countable chain condition in all finite powers. Our method shows also the finer distinction, that Martin's axiom is strictly stronger than its restriction to forcing notions whose squares satisfy the countable chain condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13108 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distinguishing Martin's axiom from its restrictions Peng, Yinhe Logic 03E50, 03E65, 03E02 We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions satisfying the countable chain condition in all finite powers. Our method shows also the finer distinction, that Martin's axiom is strictly stronger than its restriction to forcing notions whose squares satisfy the countable chain condition. |
| title | Distinguishing Martin's axiom from its restrictions |
| topic | Logic 03E50, 03E65, 03E02 |
| url | https://arxiv.org/abs/2406.13108 |