Strong partition relations below the power set: consistency, was Sierpinski right, II?
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arXiv
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| Format: | Preprint |
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1991
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| _version_ | 1866917577474703360 |
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| author | Shelah, Saharon |
| author_facet | Shelah, Saharon |
| contents | We continue here [She88] but we do not rely on it. The motivation was a conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2-> [omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section 5 we disprove this and give similar negative results. In section 3 we prove the consistency of the conjecture replacing omega_2 by 2^omega, which is quite large, starting with an Erdős cardinal. In section 1 we present iteration lemmas which are needed when we replace omega by a larger lambda and in section 4 we generalize a theorem of Halpern and Lauchli replacing omega by a larger lambda . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_9201244 |
| institution | arXiv |
| publishDate | 1991 |
| record_format | arxiv |
| spellingShingle | Strong partition relations below the power set: consistency, was Sierpinski right, II? Shelah, Saharon Logic We continue here [She88] but we do not rely on it. The motivation was a conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2-> [omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section 5 we disprove this and give similar negative results. In section 3 we prove the consistency of the conjecture replacing omega_2 by 2^omega, which is quite large, starting with an Erdős cardinal. In section 1 we present iteration lemmas which are needed when we replace omega by a larger lambda and in section 4 we generalize a theorem of Halpern and Lauchli replacing omega by a larger lambda . |
| title | Strong partition relations below the power set: consistency, was Sierpinski right, II? |
| topic | Logic |
| url | https://arxiv.org/abs/math/9201244 |