## Journal of Symbolic Logic

### Universal Structures in Power $\aleph_1$

Alan H. Mekler

#### Abstract

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 $\aleph_2$.

#### Article information

Source
J. Symbolic Logic, Volume 55, Issue 2 (1990), 466-477.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743307

Mathematical Reviews number (MathSciNet)
MR1056364

Zentralblatt MATH identifier
0702.03028

JSTOR

#### Citation

Mekler, Alan H. Universal Structures in Power $\aleph_1$. J. Symbolic Logic 55 (1990), no. 2, 466--477. https://projecteuclid.org/euclid.jsl/1183743307