Weak diamond and pcf theory
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917658077691904 |
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| author | Garti, Shimon |
| author_facet | Garti, Shimon |
| contents | We obtain bounds on the cardinality of $pcf(\mathfrak{a})$ from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\aleph_δ$ for which $2^{\aleph_δ}<\aleph_{(|δ|^{+3})}$. For example, if every limit cardinal is a strong limit cardinal then this bound holds at a class of singular cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak diamond and pcf theory Garti, Shimon Logic 03E04 We obtain bounds on the cardinality of $pcf(\mathfrak{a})$ from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\aleph_δ$ for which $2^{\aleph_δ}<\aleph_{(|δ|^{+3})}$. For example, if every limit cardinal is a strong limit cardinal then this bound holds at a class of singular cardinals. |
| title | Weak diamond and pcf theory |
| topic | Logic 03E04 |
| url | https://arxiv.org/abs/2405.03142 |