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Algebraic systems, relational structures. As considered in model theory, a structure (or a model) is a set endowed with a family of finitary relations and functions (operations). In some contexts, these can be represented by relational structures with some of the $(n+1)$-ary relations being viewed as $n$-ary functions. As considered in universal algebra, an algebraic structure is a structure with operations only.

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Is there a relational countable ultra-homogeneous structure whose countable substructures do...

An example is the "complete rainbow graph without monochromatic triangles". Let $L = \{R_i : i \in \omega\}$ be a language consisting of $\omega$-many binary relation symbols $R_i$, and take the class …
Rob Sullivan's user avatar