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arXiv · 1610.00319

Namba forcing, weak approximation, and guessing

Sean Cox·John Krueger
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Abstract

We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\textsf{IGMP}$, $\textsf{GMP}$ together with $2^ω\le ω_2$ is consistent with the existence of an $ω_1$-distributive nowhere c.c.c. forcing poset of size $ω_1$. We introduce the idea of a weakly guessing model, and prove that many of the strong consequences of the principle $\textsf{GMP}$ follow from the existence of stationarily many weakly guessing models. Using Namba forcing, we construct a model in which there are stationarily many indestructibly weakly guessing models which have a bounded countable subset not covered by any countable set in the model.

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Sean Cox, John Krueger. 2018-05-25. Namba forcing, weak approximation, and guessing. https://doi.org/10.1017/jsl.2018.30

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