Guessing models imply the singular cardinal hypothesis

John Krueger

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arXiv · 1903.10476

Guessing models imply the singular cardinal hypothesis

John Krueger

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Abstract

In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets which have the $\omega_1$-approximation property also have the countable covering property. These results solve open problems of Viale and Hachtman-Sinapova.

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John Krueger. 2019-03-25. Guessing models imply the singular cardinal hypothesis. https://arxiv.org/abs/1903.10476

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