# universal structure

Let $L$ be a first order language, and let $R$ be an elementary class of $L$-structures. Let $\kappa$ be a cardinal. $R_{\kappa}$ be the set of structures from $R$ with cardinality less than or equal to $\kappa$.

Let $M\in R_{\kappa}$. Suppose that for every $N\in R_{\kappa}$ there is an embedding of $N$ into $M$. Then we say $M$ is .

Title universal structure UniversalStructure 2013-03-22 13:23:09 2013-03-22 13:23:09 Timmy (1414) Timmy (1414) 4 Timmy (1414) Definition msc 03C50 msc 03C52 universal