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arXiv · 1605.00605

Universal graphs at $\aleph_{\omega_1+1}$

Jacob Davis
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Abstract

Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$. The same technique will work for any uncountable cardinal in place of $\omega_1$.

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Jacob Davis. 2016-05-02. Universal graphs at $\aleph_{\omega_1+1}$. https://arxiv.org/abs/1605.00605

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