Consistency of square bracket partition relation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912805120114688 |
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| author | Shelah, Saharon |
| author_facet | Shelah, Saharon |
| contents | Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [λ]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} = \aleph_m) + \aleph_l \to [\aleph_k]^2_{n, 2})$, for suitable $k < l < m$. So we improve in three respects: the continuum may be small (e.g. not a weakly Mahlo), we use no large cardinal, and the cardinals $λ$ involved are $ < 2^{\aleph_0}$ after the forcing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Consistency of square bracket partition relation Shelah, Saharon Logic Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [λ]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} = \aleph_m) + \aleph_l \to [\aleph_k]^2_{n, 2})$, for suitable $k < l < m$. So we improve in three respects: the continuum may be small (e.g. not a weakly Mahlo), we use no large cardinal, and the cardinals $λ$ involved are $ < 2^{\aleph_0}$ after the forcing. |
| title | Consistency of square bracket partition relation |
| topic | Logic |
| url | https://arxiv.org/abs/2601.02923 |