Weak diamond and pcf theory

Shimon Garti

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arXiv · 2405.03142

Weak diamond and pcf theory

Shimon Garti

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Abstract

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 $\aleph_\delta$ for which $2^{\aleph_\delta}<\aleph_{(|\delta|^{+3})}$. For example, if every limit cardinal is a strong limit cardinal then this bound holds at a class of singular cardinals.

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Shimon Garti. 2024-05-06. Weak diamond and pcf theory. https://arxiv.org/abs/2405.03142

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