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arXiv · 2302.05634

Complete Bipartite Partition Relations in Cohen Extensions

Dávid Uhrik
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Abstract

We investigate the effect of adding $\omega_2$ Cohen reals on graphs on $\omega_2$, in particular we show that $\omega_2 \to (\omega_2, \omega : \omega)^2$ holds after forcing with $\mathsf{Add}(\omega, \omega_2)$ in a model of $\mathsf{CH}$. We also prove that this results is in a certain sense optimal as $\mathsf{Add}(\omega, \omega_2)$ forces that $\omega_2 \not\to (\omega_2, \omega : \omega_1)^2$.

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Dávid Uhrik. 2023-02-11. Complete Bipartite Partition Relations in Cohen Extensions. https://arxiv.org/abs/2302.05634

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