publication . Preprint . 2016

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

Davis, Jacob;
Open Access English
  • Published: 02 May 2016
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 $\omega_1$.
free text keywords: Mathematics - Logic, 03E35, 03E55, 03E75
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