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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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Shape of axioms in algebraic structures

x = "preservation". Usually one is motivated to study a structure because it serves as a model for something of interest. Likewise a certain statement or class of statements may have nice consequenc …
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