Universal Structures in Power $aleph_1$

Journal of Symbolic Logic 55 (2):466-477 (1990)
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It is consistent with $\neg\mathrm{CH}$ that every universal theory of relational structures with the joint embedding property and amalgamation for $\mathscr{P}^-(3)$-diagrams has a universal model of cardinality $\aleph_1$. For classes with amalgamation for $\mathscr{P}^-(4)$-diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality $\aleph_2$



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